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July 28, 2014

Homework Help: Math: Calculus

Recent Homework Questions About Calculus

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calculus
a spherical balloon filled with gas has a leak that permits the gas to escape at a rate of 1.5 cubic meters per minute. how fast is the surface area of the balloon shrinking when the radius is 4 meters?
Thursday, November 7, 2013 at 2:54pm

Calculus I
A zombie steps off a 35-foot wall by mistake, landing in the river below. How long will it take the zombie to fall?
Wednesday, November 6, 2013 at 11:55pm

calculus HELP!
An elevator in a high rise building accelerates and decelerates at the rate of 1 foot per second squared. Its maximum speed is 8 feet per second. It starts from rest, accelerates to its maximum speed and stays at that maximum speed until it approaches its destination where it ...
Wednesday, November 6, 2013 at 9:53pm

math calculus
A person stands on a bridge that is 100 feet above a river. If she drops a pebble how fast is it moving after 2 seconds? How long does it take the pebble to reach the river below? She has another pebble that she tosses up with initial speed of 8 feet per second. It goes up, ...
Wednesday, November 6, 2013 at 9:52pm

Help! Calculus
An elevator in a high rise building accelerates and decelerates at the rate of 1 foot per second squared. Its maximum speed is 8 feet per second. It starts from rest, accelerates to its maximum speed and stays at that maximum speed until it approaches its destination where it ...
Wednesday, November 6, 2013 at 9:46pm

calculus HELP!
A person stands on a bridge that is 100 feet above a river. If she drops a pebble how fast is it moving after 2 seconds? How long does it take the pebble to reach the river below? She has another pebble that she tosses up with initial speed of 8 feet per second. It goes up, ...
Wednesday, November 6, 2013 at 9:45pm

Calculus
Evaluate the surface integral. the double integral of (x^2 + y^2 + z^2)dS over Region S. S is the part of the cylinder that lies between the planes z = 0 and z = 5, together with its top and bottom disks Can anyone help?
Wednesday, November 6, 2013 at 9:06pm

calculus
A Ferris wheel with a radius of 13 m is rotating at a rate of one revolution every 2 minutes. How fast is a rider rising when the rider is 25 m above ground level?
Wednesday, November 6, 2013 at 7:47pm

Calculus
Suppose that f(x)=3x^3+3x. Find all critical values of f. Then use interval notation to state when f(x) is increasing and when f(x) is decreasing and to state when f(x) is concave up and concave down. Find the local maxima and local minima. Find all vertical and horizontal ...
Wednesday, November 6, 2013 at 3:40pm

Calculus
Suppose that f(x)=ln(3+x^2). Use interval notation to state when f(x) is concave up and concave down. Then find all inflection points for f(x).
Wednesday, November 6, 2013 at 3:37pm

multivariable calculus
Studying for a test, and saw this: Find the center of mass of the hemisphere x^2 + y^2 + z^2 = a^2; z>=0 if it has constant density. Any ideas?
Wednesday, November 6, 2013 at 2:46pm

calculus
A ladder of 85 m length is resting against a wall. If it slips 7 m down the wall, then how far is the bottom from the wall if it was initially 40 m away from it.
Wednesday, November 6, 2013 at 2:40pm

Calculus - #6
If the following function is continuous, then what is the value of b? g(f)={2t^2+2t-24 if f≠3 {b if f=3 0 3 7 14 None of these If the following function is continuous, then what is the value of a? h(f)={2t+b if f<0 {2cos(f)-3 if 0≤f≤(pi/2) {asin(f)+5b if f...
Wednesday, November 6, 2013 at 11:57am

Calculus - #5
If h(x) is equal to (x^2-4)/(x+2)when x ≠ –2, and h(x) is continuous for all real numbers, then what is the value of h(–2)? 0 –2 –4 2 This is impossible. There is an infinite discontinuity at x = –2.
Wednesday, November 6, 2013 at 11:34am

Calculus - #4
Suppose g(x)={1/(x-2) if x<1 {2x-4 if x≥1 The best description concerning the continuity of g(x) is that the function: is continuous. has a jump discontinuity. has an infinite discontinuity. has a removable discontinuity. None of these
Wednesday, November 6, 2013 at 11:31am

Calculus - #3
Suppose g(x)={1/(x-2) if x<1 {2x-3 if x≥1 The best description concerning the continuity of g(x) is that the function: is continuous. has a jump discontinuity. has an infinite discontinuity. has a removable discontinuity. None of these
Wednesday, November 6, 2013 at 11:26am

Calculus - #2
Suppose g(x)={x^2+2x+1/x+1 if x<1 {2x if x≥1 The best description concerning the continuity of g(x) is that the function: is continuous. has a jump discontinuity. has an infinite discontinuity. has a removable discontinuity. has both infinite and removable ...
Wednesday, November 6, 2013 at 10:42am

Calculus - #1
Suppose g(x)={1/x+1 if x<1 {2x-1 if x≥1 The best description concerning the continuity of g(x) is that the function: is continuous. has a jump discontinuity. has an infinite discontinuity. has a removable discontinuity. has both jump and infinite discontinuity.
Wednesday, November 6, 2013 at 10:37am

Calculus-Aproximate Areas
A ball is thrown upward at time t = 9 seconds on planet Ubuntu, and its acceleration from time t=9 seconds to t=21 seconds is given by the function . a(t) = (3) / (t - 8) m/s^2 Use 4 time intervals of equal length to overestimate, and then underestimate, the relative velocity ...
Wednesday, November 6, 2013 at 8:42am

Calculus
Answer the following questions for the function f(x)=(x^3-9x^2+27x-27)/(x^2-6x+8) defined on the interval [-14, 22]. Enter points, such as inflection points in ascending order. A. The function f(x) has vertical asymptotes at _______ and ________. B. f(x) is concave down on the...
Tuesday, November 5, 2013 at 12:28pm

Calculus
Consider the function f(x)=4(x-5)^(2/3). For this function, there are two important intervals: (-Inf, A) and (A, Inf) Where A is a critical number. Find A
Tuesday, November 5, 2013 at 12:18pm

Calculus!!!
A piece of wire 28 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (a) How much wire should be used for the square in order to maximize the total area? (b) How much wire should be used for the square in order to minimize the ...
Tuesday, November 5, 2013 at 7:35am

calculus
using 5 rectangles what is the area under a curve using the function f(x)=3x+4 with boundries at [0,2]
Tuesday, November 5, 2013 at 2:52am

calculus
using 5 rectangles what is the area under a curve using the function f(x)=x with boundries at [-2,3]
Tuesday, November 5, 2013 at 2:50am

calculus
using 5 rectangles what is the area under a curve using the function f(x)=3x+4 with boundries at [0,2]
Tuesday, November 5, 2013 at 2:49am

Calculus
I'm struggling some with the us of trigonomic properties. The problem is integral sin(2x)sec(x) dx and I dont understand how sin(2x)sec(x) simplifies into 2sin(x).
Monday, November 4, 2013 at 9:49pm

Calculus-Aproximate Areas
Estimate the area under the graph of f(x)=sin(pix) from x=0 to x=1 using the areas of 3 rectangles of equal width, with heights of the rectangles determined by the height of the curve a a) left endpoint: b) right endpoint:
Monday, November 4, 2013 at 8:55pm

Calculus-Aproximate Areas
Estimate the area under the graph of f(x)=sin(pix) from x=0 to x=1 using the areas of 3 rectangles of equal width, with heights of the rectangles determined by the height of the curve at a) left endpoint: b) right endpoint:
Monday, November 4, 2013 at 7:03pm

Calculus
Find two positive numbers that satisfy the requirements: "The product is 147 and the sum of the first number plus three times the second number is a minimum."
Monday, November 4, 2013 at 5:33pm

English
What is the gerund phrase and noun function of the gerund in these sentences: 1.Brett earns his income by repairing cars. 2.I enjoy playing the piano. 3.Her favorite pastime is entertaining friends. 4.She is successful in mimicking others' voices. 5.He must like studying ...
Monday, November 4, 2013 at 5:13pm

Calculus-Approximate areas
Estimate the area under the graph of f(x)= x^2 + 3 x from x=1 to x=10 using the areas of 3 rectangles of equal width, with heights of the rectangles determined by the height of the curve at a) left endpoints: b) right endpoints:
Monday, November 4, 2013 at 12:59pm

Calculus II
A cable that weighs 1.5 lb/ft is used to lift 700 lb of coal up a mineshaft that is 400 ft deep. Find the work done.
Sunday, November 3, 2013 at 5:56pm

calculus
Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = (36 − t^2)^ 1/t, [−1, 6]
Sunday, November 3, 2013 at 5:02pm

Calculus
According to the National Health Survey, the heights of adult males in the United States are normally distributed with mean 69.0 inches and standard deviation 2.8 inches. A. What is the probability that an adult male chosen at random is between 61 inches and 71 inches tall? B...
Sunday, November 3, 2013 at 3:56pm

Brief calculus
The marginal cost of producing the xth box of CDs is given by 9 − x/(x^2 + 1)^2. The total cost to produce 2 boxes is $1,200. Find the total cost function C(x). I'm getting 9x-(1/(x^2 - 1))+1181.9 but i guess its wrong
Sunday, November 3, 2013 at 3:45pm

Calculus
A) Find the average value of f(x)=x^3-x+1 on the interval (0,2) B) Find c so that f(c)equals the average value
Sunday, November 3, 2013 at 3:44pm

Calculus - Compound Interest
Recently, a certain bank offered a 10-year CD that earns 8.93% compounded continuously. a) If $20,000 is invested in this CD, how much will it be worth in 10 years? Ans: I used the formula A = Pe^(rt) to get the answer $48,848.92 b)How long will it take for the account to be ...
Sunday, November 3, 2013 at 3:34pm

Pre-Calculus
How is -16/(4x+6)^5 and -1/(2(2x+3)^5) equivalent? I think -1/2(2x+3)^5 is the more simplified version of the two, but I just can't figure out how -16/(4x+6)^5 simplifies to -1/(2(2x+3)^5). please explain
Sunday, November 3, 2013 at 1:36pm

calculus
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = e−x − e−7x, [0, 1]
Sunday, November 3, 2013 at 1:06pm

Calculus
Given V(t) = 125,000e^(t/8) find V('t)
Sunday, November 3, 2013 at 12:54pm

Calculus
A 17 foot ladder is leaning against a wall. The bottom of the ladder is moving out away from the wall at 0.6 feet per second. The top of the ladder then begins sliding down the wall. How fast is the top of the ladder going when the bottom is 8 feet away from the wall?
Sunday, November 3, 2013 at 12:39pm

calculus
A piece of wire 18 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (a) How much wire should be used for the square in order to maximize the total area?
Sunday, November 3, 2013 at 10:35am

calculus
A Ferris wheel with a radius of 13 m is rotating at a rate of one revolution every 2 minutes. How fast is a rider rising when the rider is 18 m above ground level?
Sunday, November 3, 2013 at 10:33am

calculus
At noon, ship A is 150 km west of ship B. Ship A is sailing east at 25 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM?
Sunday, November 3, 2013 at 10:32am

calculus
At noon, ship A is 150 km west of ship B. Ship A is sailing east at 25 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM?
Sunday, November 3, 2013 at 10:32am

Calculus-Newton Method Approximation
Use Newton's method to approximate the positive value of x which satisfies x=2.3cosx Let x0=1 be the initial approximation. Find the next two approximations, x_1 and x2, to four decimal places each.
Friday, November 1, 2013 at 10:10pm

Calculus-Applied Optimization Problem
The manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 425 dollars per month. A market survey suggests that, on average, one additional unit will remain vacant for each 9 dollar increase in rent. Similarly, one additional ...
Thursday, October 31, 2013 at 9:27pm

Pre-Calculus
I don't understand,please be clear! Prove that each equation is an identity. I tried to do the problems, but I am stuck. 1. cos^4 t-sin^4 t=1-2sin^2 t 2. 1/cos s= csc^2 s - csc s cot s 3. (cos x/ sec x -1)- (cos x/ tan^2x)=cot^2 x 4. sin^3 z cos^2 z= sin^3 z - sin^5 z
Thursday, October 31, 2013 at 7:01pm

Calculus-Applied Optimization Quiz Problem
A rancher wants to fence in a rectangular area of 23000 square feet in a field and then divide the region in half with a fence down the middle parallel to one side. What is the smallest length of fencing that will be required to do this?
Thursday, October 31, 2013 at 6:38pm

Calculus-Applied Optimization Problem
If a total of 1900 square centimeters of material is to be used to make a box with a square base and an open top, find the largest possible volume of such a box.
Thursday, October 31, 2013 at 5:09pm

Pre-Calculus
Prove that each equation is an identity. I tried to do the problems, but I am stuck. 1. cos^4 t-sin^4 t=1-2sin^2 t 2. 1/cos s= csc^2 s - csc s cot s 3. (cos x/ sec x -1)- (cos x/ tan^2x)=cot^2 x 4. sin^3 z cos^2 z= sin^3 z - sin^5 z
Thursday, October 31, 2013 at 10:03am

Calculus
How to integrate dx/(4-5 sin x) using t-substitution method(i.e. taking tan x/2=t)?
Thursday, October 31, 2013 at 8:15am

Calculus
What is the radius of convergence of the power series (((2n)!x^(n))/((2n-1)!)), and what is its interval of convergence? I used the ratio test and found that the radius of convergence is 0, as it is impossible for the absolute value of infinity to be less than 1. I am not sure...
Thursday, October 31, 2013 at 2:39am

Pre-Calculus
Let f(x) = [(√x)-7]/[(√x)+7]. What is f'(x)? What is the easiest way to find the derivative of this? Should I remove all the radicals and use quotient rule, like f'(x)= ((x^0.5) + 7)(0.5x^-0.5) - ((x^0.5)-7)(0.5x^-0.5) / ((x^0.5) + 7)^2 Is this right? How ...
Thursday, October 31, 2013 at 2:38am

Calculus
How do I find the radius of convergence of a series where n=1 to infinity of (14^(n)x^(n)n!)? I have tried using the ratio test but I eventually get to this step: lim as n approaches infinity of absolute value of (14x(n+1)), which equal infinity. How am I to set the absolute ...
Thursday, October 31, 2013 at 1:53am

Calculus-concavity and graphing
(2x+1)/(8x+1) f is increasing for x: f is decreasing for x: find local max/min:
Wednesday, October 30, 2013 at 9:50pm

calculus
i need help with proving five steps of l hospitals rule for (ex^2-1)/x
Wednesday, October 30, 2013 at 3:54pm

Calculus-Applied Optimization Problem:
Find the point on the line 6x + 3y-3 =0 which is closest to the point (3,1). Note: Your answer should be a point in the xy-plane, and as such will be of the form (x-coordinate,y-coordinate)
Wednesday, October 30, 2013 at 12:42pm

Calculus
s=çdx/(4+5cos x). By using t-substitution, i.e. t=tan(x/2) we get cos x=(1-t^2)/(1+t^2) and dx=2dt/(1+t^2). Substituting in s and simplifying, we get s= 2çdt/4(1+t^2)+5(1-t^2)=2​29;çdt/(9-t^2). Using standard result çdx/(a...
Wednesday, October 30, 2013 at 4:42am

Calculus
A spotlight on the ground is shining on a wall 12m away. If a woman 2m tall walks from the spotlight toward the building at a speed of 0.6m/s, how fast is the length of her shadow on the building decreasing when she is 2m from the building?
Wednesday, October 30, 2013 at 3:46am

Calculus (integrals)
Find the integral:8x^7+6/(x^8+6x)^2 I got ln(x^8+6x)^2 but apparently that is wrong.
Tuesday, October 29, 2013 at 10:21pm

calculus
Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 3m/s, how fast is the area of the spill increasing when the radius is 15m?
Tuesday, October 29, 2013 at 7:52pm

Calculus
Consider the function f(x)=-2x^3+33x^2-108x+2. For this function, there are three important intervals: (-Inf,A], [A,B], [B,Inf) where A and B are the critical points. Find A and B and for each of the important intervals, tell whether f(x) is increasing or decreasing.
Tuesday, October 29, 2013 at 11:47am

Calculus
Find the absolute maximum and absolute minimum values of the function f(x)=x^3+6x^2-63x+4 on each of the indicated variables. Enter DNE for does not exist. (A) Interval = [-8,0] Absolute maximum = Absolute minimum = (B) Interval = [-5,4] Absolute maximum = Absolute minimum = (...
Tuesday, October 29, 2013 at 11:41am

Calculus
The function f(x)=-2x^3+30x^2-96x+8 has one local minimum & one local maximum. This function has a local minimum at x equals ______ with value __________ and a local maximum at x equals _______ with value __________ .
Tuesday, October 29, 2013 at 11:35am

Calculus
Suppose f(x)= 7-8x^2, by the Mean Value Theorem, we know there exists a c in the open interval (-2,5) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.
Tuesday, October 29, 2013 at 11:14am

brief calculus
I have everything right but the last question asking how many cases per week The consumer demand equation for tissues is given by q = (97 − p)^2, where p is the price per case of tissues and q is the demand in weekly sales. (a) Determine the price elasticity of demand E ...
Tuesday, October 29, 2013 at 1:13am

brief calculus
I found that c=1 but i can't get the other two questions The velocity of a particle moving in a straight line is given by v(t) = t2 + 7. (a) Find an expression for the position s after a time t . s(t) = _____ + C (b) Given that s = 1 at time t = 0, find the constant of ...
Monday, October 28, 2013 at 11:15pm

Calculus
List the critical numbers of the following function in increasing order. Enter N in any blank that you don't need to use. f(x) = (6x+6)/(5x^2+5x+5)
Monday, October 28, 2013 at 9:48pm

Calculus
Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function. If there are multiple values, separate them with commas; enter N if there are no such values. f(x)= x^2-10x+3, [0,10]
Monday, October 28, 2013 at 9:46pm

calculus
find Arc Length of (9-x^(2/3))^(3/2) I square the second derivative and have it under the square root but then get stuck at (-9x^-1)+x^(-1/3)+1 Help?
Monday, October 28, 2013 at 8:01pm

calculus
find 3 positive real numbers whose sum is 500 and whose product is as large as possible.
Monday, October 28, 2013 at 3:17am

calculus
A trough is 6 feet long and has ends that are isosceles triangles that are 1 foot high and 3.5 feet wide. If the trough is being filled at a rate of 9 cubic feet per minute, how fast is the height of the water increaseing when the height is 5 inches?
Monday, October 28, 2013 at 12:54am

calculus
A street light is at the top of a 15.000 ft. tall pole. A man 6.300 ft tall walks away from the pole with a speed of 6.000 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 45.000 feet from the pole?
Monday, October 28, 2013 at 12:53am

calculus
A plane that is flying horizontally at an altitude of 6 kilometers and a speed of 570 kilometers per hour passes directly over a radar station. How fast is the distance between the plane and the radar station increasing when the distance between the two is 14 kilometers
Monday, October 28, 2013 at 12:52am

brief calculus
Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope 6/x
Sunday, October 27, 2013 at 6:16pm

Pre-Calculus
Transform the expression from the left to the right. Tan A+ CotA to cscAsecA
Sunday, October 27, 2013 at 3:28pm

Calculus Related
tinyurl[dot]com/osguqrd Replace [dot] with a . Please provide an answer to the question in the link above.
Sunday, October 27, 2013 at 5:50am

calculus
if a snowball melts so that its surface area decreases at a rate f 1cm^2/min, find the rate at which the diameter decrease when the diameter is 10cm?
Friday, October 25, 2013 at 6:56pm

Calculus
f(x)=x^3-(4/x) find [f^(-1)(x)]' at x=6
Thursday, October 24, 2013 at 10:36pm

Calculus Homework
Find the largest region over which the function f is increasing or decreasing, for: f(x):(x-4)/(x+8) f is increasing for x=
Wednesday, October 23, 2013 at 7:45pm

Calculus-Mean Value Theorem
Find the function G(x) whose graph passes through (pi/38,-12)and has f(x) as its derivative: G(x)= I already found which is: F(x)=76(1/-19)cos(19x)+C
Wednesday, October 23, 2013 at 5:30pm

Calculus
Romat 421 (a fictitious substance) decays by about 1.5% every day. How much of a 80 pound sample remains after 5days?
Wednesday, October 23, 2013 at 4:15pm

Calculus
The population in certain country is growing at the rate of 7 % a year . If the population in the year 1995 was 190 million, (a)determine an exponential expression representing the population as a function of the year. (b) What will the population be in 2005 ? (c) What was the...
Wednesday, October 23, 2013 at 1:08am

Practice Exam Calculus
f(x) = 6sqrt{x}- 9x n the interval [1,9]. f(c)=f(9)-f(1)/9-(1)=? Verify that the conclusion of the Mean Value Theorem holds by computing Now find,c in (1, 9) so that f'(c) equals the answer you just found. c=?
Tuesday, October 22, 2013 at 8:58pm

calculus
(A) Consider the wave equation with c=1, l=1, u(0,t)=0, and u(l,t)=0. The initial data are: f(x)=x(1-x)2, g(x)=sin2(pi x). Find the value of the solution at x=0, t=10, and at x=1/3, t=0. Find the value of the solution at x=1/2, t=2. (B) Suppose that l=2, c=1/2. Draw the domain...
Tuesday, October 22, 2013 at 4:33pm

Calculus
x=7t−t^2,y=4t^(3/2) from the point (0,0) to the point (12,32), you'd have to compute integral b to a f(t)dt where a= b= f(t) =
Tuesday, October 22, 2013 at 2:36pm

Calculus
Use continuity to evaluate. as x approaches 2, lim arctan((2x^2-8)/(3x^2-6x))
Tuesday, October 22, 2013 at 12:45pm

Calculus
Evaluate the limit. as x approaches infinity, lim sqrt(x^2+6x+3)-x
Tuesday, October 22, 2013 at 12:43pm

Calculus Please Help?
A hawk flying at 25 m/s at an altitude of 150 m accidentally drops its prey. The parabolic trajectory of the falling prey is described parametrically by x=25t,y=150−4.9t^2 until it hits the ground. The variable x represents the horizontal distance traveled by the prey ...
Tuesday, October 22, 2013 at 12:00pm

Calculus
To find the length of the curve defined by x=7t−t^2,y=4t^(3/2) from the point (0,0) to the point (12,32), you'd have to compute çb to a f(t)dt where a= b= f(t) =
Tuesday, October 22, 2013 at 9:08am

Calculus
If C(x) = 18000 + 400x − 2.2x^2 + 0.004x^3 is the cost function and p(x) = 2800 − 7x is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)
Monday, October 21, 2013 at 8:53pm

Calculus
If C(x) = 18000 + 400x − 2.2x^2 + 0.004x^3 is the cost function and p(x) = 2800 − 7x is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)
Monday, October 21, 2013 at 8:52pm

calculus
Let y =x arcsin x, x is an element of ]-1, 1[. Show that d^2y/dx^2 = 2-x^2/(1-x^2)^3/2
Monday, October 21, 2013 at 8:25pm

Calculus
Find the limit: as x approaches 0 lim((5/x)-(5/sin(x))
Monday, October 21, 2013 at 3:02pm

Calculus
Simplify cos(sin^(-1)x)
Monday, October 21, 2013 at 2:54pm

Calculus
Simplify sin(tan^(-1)x)
Monday, October 21, 2013 at 2:54pm

Calculus
y = tan^-1(sqrt(5x^2-1)) find dy/dx
Monday, October 21, 2013 at 2:52pm

Calculus
If f(x) = 2sin(5x)arcsin(x), find f'(x).
Monday, October 21, 2013 at 2:37pm

Calculus
Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it diverges to infinity, state your answer as INF. If it diverges to negative infinity, state your answer as MINF. If it diverges without being infinity or negative infinity, state ...
Sunday, October 20, 2013 at 8:58pm

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