# Calculus

Calculus
An upright cylindrical tank with radius 3 m is being filled with water at a rate of 4 m3/min. How fast is the height of the water increasing?

Calculus
The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the diameter is 100 mm? Evaluate your answer numerically.

Calculus
What how do you compute the sum of 1/2 + 1/4 + 1/8 + 1/16 + 1/32 +++ 1/2N ? ..

Calculus
What how do you compute the sum of 1/2 + 1/4 + 1/8 + 1/16 + 1/32 +++ 1/2N ?

calculus
A spherical balloon , initially inflated to a volume of over 30000 cubic meters, springs a leak which causes the radius to decrease at a rate of 2 meters per minute. At the instant when the radius is 3 meters , how fast ( in cubic meters per minute ) is the hor air escaping ...

calculus
One bicycle is east of an intersection , and it is travelling towards the intersection of 9 miles per hour. at the same time a second bicycle is south of the intersection , and it is travelling away from the intersection at the rate of 10 miles per hour. Is the distance ...

Calculus
Given the graph of f'(x) with f(x) continuous on all reals, find the intervals f(x) is concave up and down and find the X values of the points of inflection. I did points -2 concave down to 2 then concave up 4.

Calculus
Given the graph of f'(x) with f(x) continuous on all reals, find the intervals f(x) is concave up and down and find the x values of the points of inflection.

calculus
Evaluate the double integral ∫∫ y dA over D, where D is the top half of the disk with center the origin and radius 5?

Calculus 2
Determine the first three terms of the power series representations for the following functions: a) 2/(1+x)^3 b) 1/1+x^2 c) ln(1+x)

Calculus 2 - Indeterminant forms
lim (2^x-3^x)/(cos(x)-1) x->0 The answer the book has for this is "diverges." I know I'm supposed to use L'Hospitals' rule, but I'm not sure how. Can you walk me through the steps?

Pre-Calculus
A drug manufactured by a pharmaceutical company is sold in bulk at a price of \$150 per unit. The total production cost (in dollars) for x units in one week is C(x) = 0.02x^2 + 100x + 3000. How many units of the drug must be manufactured and sold in a week to maximize the ...

Calculus
A rectangular storage container with an open top is to have a volume of 10 . The length of its base is twice the width. Material for the base costs \$12 per square meter. Material for the sides costs \$5 per square meter. Find the cost of materials for the cheapest such container.

Calculus
How do I find the derivative of e^y -y=x^2 -2? Do I use chain rule with -d/dy or -d/dx or dy/dx? And then how do I find the slope of the graph if the point's at (2,0)?

Calculus
Oblique tracking. A ship leaves port traveling southwest at a rate of 12 mi/hr. at noon, the ship reaches its closest approach to a radar station, which is on the shor 1.5 miles from the port. if the ship maintains its speed and course, what is the rate of change of the ...

Calculus
How many units should this company sell to maximize their revenue if the revenue function was -(x^2/100)+50x using derivatives?

Calculus
If the instantaneous rate of change of f(x) at (2,-4) is 5, write the equation of the line tangent to the graph of f(x) at x=2.

Calculus
How do you find the original function given a point (a,b) and the equation of the line tangent to the graph of f(x) at (a,b). For example: The point is (4,-11) and 7x-3y=61 is the equation of the line tangent to the graph of f(x)

Calculus
How do you find the original function given the equation of a tangent line and two points?

Calculus
Imagine slicing through a sphere with a plane (sheet of paper). the smaller piece produced is called a radius of the sphere. Its volume is V=(pi)h^2(3r-h)/3, where r is the radius of the sphere and h is the thickness of the cap. find dr/dh for a sphere with a volume of 5pi/3m^...

Calculus
If an arrow is shot upward on Mars with a speed of 54 m/s, its height in meters t seconds later is given by y = 54t − 1.86t2 (i) [1, 2](ii) [1, 1.5] (iii) [1, 1.1] (iv) [1, 1.01] (v) [1, 1.001] (b) Estimate the speed when t = 1.

calculus 3
A pilot is flying a Cessna airplane at 180 mph (airspeed).He would like to fly in the direction N45W, but there is a 32 mph wind in the S60W direction.What direction should the pilot set his course for in order to fly along his desired track? What will his speed relative to ...

calculus 3
A pilot is flying a Cessna airplane at 180 mph (airspeed).He would like to fly in the direction N45W, but there is a 32 mph wind in the S60W direction.What direction should the pilot set his course for in order to fly along his desired track? What will his speed relative to ...

Calculus
Give an example of a function that is integrable on the interval [-1,1], but not continuous on [-1,1]. Explain.

CAlculus
Find the linear function satisfying the given conditions. g(2) = 9 and the graph of g is perpendicular to the line 4x − 2y = 3. g(x) =

Calculus
Several math students are taking a break from their studies by visiting a playground. One student pushes the others on a merry-go-round. The diameter of the merry-go-round is 3.0 m, and the student pushes with a force of 50 N along the purple vector shown in the diagram. Merry...

Calculus
Hi, could someone please help me with this question? Thanks Calculate the Maclaurin series of f(x)=4x^3*sin(x^4). Explicitly use the Maclaurin series for sine. Using this series for f(x), verify that the integral of 4x^3*sin(x^4)dx=-cos(x^4)+C.

Calculus and Vectors
Determine the net result of a 35 N force and a 20 N force acting on an object at an angle of 125° to each other, using components. I know that when I draw the vectors, I use parallelogram law to determine the complimentary angle, and I got 55degrees. However, on the answers, ...

Pre-calculus
Find the center radius and equation of a circle in standard form given the following conditions: 1. Tangent to 3x+2y=0 at the point (0,0) and passing through (1,-1) and (6,0)

Pre-calculus
A ball is thrown from an initial height of 1 meter with an initial upward velocity of 9 m/s. The ball's height h (in meters) after t seconds is given by the following h=1+9t-5t^2 Find all the values of the t for which the ball's height is 4 meters.

pre-calculus
I have absolutely no idea even where to start. Please help! The carnival has come to town with a ferris wheel that has a radius of 30 feet. People get on when passenger compartments are at the lowest, 2 feet off the ground. The wheel makes a full revolution in 20 seconds. ...

Math (Calculus Optimization)
An oil field contains 8 wells, which produce a total of 1600 barrels of oil per day. For each additional well that is drilled, the average production per well decreases by 10 barrels per day. How many additional wells should be drilled to obtain the maximum amount of oil per ...

Physics, Calculus
if an aircraft flying at 250km/h at bearing N 45East for 1 hour meets a wind from the NW at 50km/h, then how long will it take to fly the full 550km maintaining its N45E bearing to the ground with this wind blowing?

calculus
Find the constant a such that the function is continuous on the entire real line g(x)=x^2-a^2/x-a if x doesn't equal a 6 if x=a

Calculus
What is the best substitution to make to evaluate the integral of the quotient of cosine of 2 times x and the square root of the quantity 5 minus 2 times the sine of 2 times x, dx? u = sin(2x) u = cos(2x) u = 2x u = 5 − 2sin(2x)

Pre-Calculus 12
how to solve 3^(x-2) = 5^x

Calculus
The shoreline of a lake is a circle with diameter 3 km. Peter stands at point E and wants to reach the diametrically opposite point W. He intends to jog along the north shore to a point P and then swim the straight line distance to W. If he swims at a rate of 3 km/h and jogs ...

Math/Pre-calculus
Assume that the number of bacteria follows an exponential growth model: P(t)=P0e^k/t. The count in the bacteria culture was 400 after 10 minutes and 1500 after 35 minutes. (a) What was the initial size of the culture? (b) Find the population after 85 minutes. (c) How many ...

pre-calculus
x^2+6x+8y=7 Find the: Direction: Vertex: Focus: Axis of Symmetry: Directrix:

Calculus
Find the limit x->pi/2^+ tan(x) I know the answer is -∞, but I don't understand why. When I simplify to sin(x)/cos(x), I get 1/0^+.

Multivariable calculus
I have to show that the relative error of the product of two positive numbers is aproximately to the sum of the relative errors of its factors. My teacher told me to use first order approximation, but I don't know how to use it.Please help

Calculus
two sides of a triangle have lengths 15 m and 20 m. the angle between them is increasing at a rate of pi/90 rad/s. At what rate is the area changing when the angle between the two given sides is pi/3 Can't seem to figure it out!

Calculus
Hi, I have this question here that I'm not sure about. Any help is appreciated. Evaluate the integral from 1 to 3 of dx/(x-2). This seems like it should be really simple- is it 0?

Calculus
S=integral sign S3x(4-x^2)^1/2 use trig substitution I am confused I got x sin(sin^-1(x/2))+cos(sin^-1(x/2))

Calculus
(1,1)(2,1)(2,3) mirror Revolve around y-axis. solve with Shell and washer please and thank you! Made a correction for washer would R(x)=2x-1 ? what about r(x)

Calculus
(1,1)(2,1)(2,3) mirror around y-axis & revolve solve with Shell and washer please and thank you

Multivariable calculus
Hello, I have the next exercise about chain rule in multivariable calculus: I have to show that the differential equation: y(dz/dx)-x(dz/dy) = (y-x)z can be change to the equation: (dw/dv) = 0 using the new variables: u= (x^2)+(y^2) v = (1/x)+(1/y) w = ln(z)-(x+y) For that I ...

Calculus
the region D is the triangle with vertices (1,1) (3,1) (3,2) about the y-axis find r(x) and h(x) using the shell method. My teacher got r(x)=x and h(x)=(1/2x+1/2)-1 but how did he get the equation for h(x)??

Pre-Calculus
a ferris wheel is elevated 1 meter above ground. When car reaches the highest point of the Ferris wheel, it's altitude from ground level is 31 metres. How far away from the center, horizontally, is the car when it is at an altitude of 25 meters?

Pre-Calculus 12
I am refering to the question posted on Tuesday, June 6, 2017 at 8:26pm. "how to graph y= (x^2-3x-10)/(x-2)" This is the reply I got: Pre-Calculus 12 - Damon, Tuesday, June 6, 2017 at 9:21pm (x-5)(x+2)/(x-2) well we know it is 0 at x = 5 and at x = -2 and we know it explodes ...

Calculus
if a penny is dropped from the top of a 320 ft. building, how fast will it be moving when it hits the ground? So we can find the speed of the penny as instantaneous rate of change of height of penny when it hits ground. Instantaneous rate of change of y with respect to x is dy...

Calculus
if a penny is dropped from the top of a 320 ft. building, how fast will it be moving when it hits the ground? v2 = u2 + 2gH, Here, u = initial velocity = 0 v = final velocity g = 32ft/s2 H= 320ft So, v2= 0 + 2 × 32 × 320 or,. v = ✓(2×32×32×2×5) or, v = 64✓5 ft/s is ...

Pre-Calculus
If sinx=-1/2 and x terminates in the third quadrant, find the exact value of tan2x.

Pre-Calculus 12
how to graph y= (x^2-3x-10)/(x-2)

Calculus II
Evaluate the integral by first performing long division on the integrated and then writing the proper fraction as a sum of partial fractions. x^4/x^2-9

Calculus II
Express the integrated as a sum of partial fractions and evaluate the integral 3x2+x+9/(x2+5)(x-6)

Calculus
The prompt for all of these question is "consider the function f(x) = sin^2(x)". Part A: Write the first four terms of the Maclaurin series for f(x). I assumed this implied non-zero terms, so I found x^2-(1/3)x^4+(2/45)x^6-1/315(x^8). I am fairly confident about this. Part B: ...

Math calculus
(2) (-1) (3)+(4)

Math A Calculus
For a =( 2 ÷3)and b=(-1÷4)..Find a).. a+b b).. | a+b | c).. Find the length of the vector i + 2j-- 2k

Calculus
I have to get the result of the serie from 1 to infinite of |sin(4n/π) +3|/ 4^n I really don't know what to do... Please I would really appreciate if anyone can help me

Calculus
Two forces act on an object at 20 degree to each other. One force has a magnitude of 200N, and the resultant has a magnitude of 340N. Determine the magnitude of the second force and the direction it makes with the resultant.

Calculus
A ship is sailing due north at 12km/h while another ship is observed 15km ahead, traveling due east at 9km/h. What is the closest distance of approach of the two ships?

Calculus
Show how the function y = e^(-x) sin x could represent damped oscillation. a) Determine the local extreme for a sequence of wavelengths. b) Show that the local maxima represent exponential decay.

Calculus
Find the area of the region between the curves y=8−x^2 y=x^2 x=−3 and x=3 I made a slight correction

Calculus
Find the area of the region between the curves y=8−x2 y=x2 x=−3 and x=3

calculus
i)f (x)=x^3 + -x^2

calculus
i)f (x )=e^x sinx

calculus
i)f(x)=(x^3 + -x^2 )(x^2 + 2)

calculus
Find the derivatives of the following function: i)y=-3x^-3 +2x^-2 + x-2

physics/calculus
can someone explain to me why the derivative and second derivative of this position vector r=ax+bty is r'=ax' +by'+ bty' ( why is there a by'...?) and r''=ax'' + cy' +cy' +cty'' ( why is there 2 cy' 's?

calculus
Use series to evaluate the limit. limit as x approach 0 [1-cos(5x)]/[1+5x-e^(5x)]

calculus
Evaluate the indefinite integral as an infinite series. [cos(x)-1]/x dx

Calculus
How do we integrate [(cosx)^2(nx)(sin(nx))]/[a-(cos(nx))] dx?

calculus
Find the radius of convergence, R,and the interval, I, of the series. starting n=1 [(x-4)^n]/(n^n)

calculus
Find the interval, I, of convergence of the series n=0 [((-1)^n)(x-5)^n]/(3n+1)

calculus
ind the radius of convergence, R,and the interval, I, of the series. n=3 [x^(n+1)]/(5n!)

Calculus
The base of a solid is a region located in quadrant 1 that is bounded by the axes, the graph of y = x^2 - 1, and the line x = 2. If cross-sections perpendicular to the x-axis are squares, what would be the volume of this solid?

Calculus
Given that the limit as h approaches 0 of (f(6 + h) - f(6))/h = -2, which of these statements must be true? 1. f'(6) exists 2. f(x) is continuous at x=6 3. f(6) < 0

Calculus
Use the midpoint rule with n=4 to approximate the region bounded by y=-x^3 and y=-x Show that the function f(x)= (integral from 2x to 5x) (1)/(t) dt is constant on the interval (0,+infinity)

One more question Calculus
write n with limit from 0 to infinity with the summation n on top and k=1 on the bottom (5+k(2/n))^10 (2/n) as a definite integral.

Write the integral in one variable to find the volume of the solid obtained by rotating the first‐quadrant region bounded by y = 0.5x2 and y = x about the line x = 5.

find the area bounded by the curves y^2=2x+6 and x=y+1

find d/dx (integral from 2 to x^4) tan(x^2) dx tan(x^4)^2*4x^3 MY ANSWER

Calculus
Use the Comparison Theorem to determine whether the following integral is convergent or divergent. S= integral sign b=infinity and a=1 S(9(cosx^2))/ (1+x^2) dx

Calculus
k(x) = f(x^4). Which of the following is k''(x)? a. 2xf''(x^2) b. 4x^2f''(x^2) c. (4x^2+2x)(f''(x^2)) d. 4x^2f''(x^2)+2f'(x^2) e. 4x^2f''(x^2)+2xf'(x^2)

Math (Calculus II) (Volume Revolution Setup)
Take the area enclosed by the curves y = sqrt(x), y = 1, and x = 4. Rotate it around the line x = 5. Find the volume. While I understand the general problem would call for the shell method ∫[a,b] 2*pi*r*h dx With r = 5 - x and h = sqrt(x) - 1 But, what happens say if the ...

Calculus
Find the area of a function using integrals that equals .5 (can range from .499 to .504) There has to be three regions for the equations

One more question Calculus
A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec2 is given by the linear graph below for the time interval [0, 30]. At t = 0, the velocity of the car is 0 and its position is 10. What is the total distance the car travels in...

Water is poured into a bucket according to the rate F(t)=(t+7)/(2+t), and at the same time empties out through a hole in the bottom at the rate E(t)=(ln(t+4))/(t+2), with both F(t) and E(t) measured in pints per minute. How much water, to the nearest pint is in the bucket at ...

Calculus really quick check
The graph of f ′(x) is continuous and decreasing with an x-intercept at x = 2. Which of the following statements must be true? Edit The graph of f has an inflection point at x = 2. The graph of f has a relative maximum at x = 2. The graph of f is always concave down. MY ...

the velocity of a particle moving along the x axis is v(t)=t^2+2t+1, with t measured in minutes and v(t) measured in feet per minute to the nearest foot find the total distance traveled by the particle from t=0 to t=2 minutes so, I took the integral of the equation so from 0 ...

Use the graph of f(t) = 2t +2 on the interval [−1, 4] to write the function F(x), where f(x)= integral from 1 to x f(t) dt f(x)=x^2+3x f(x)=x^2+2x-12 My Answer f(x)x^2+2x-3 f(x)=x^2+4x-8 Find the range of the function f(x)=integral from 0 to x (sqrt 4-t^2) dt (0, 4pi) (0, ...

f is a function that is differentiable for all reals. The value of f ′(x) is given for several values of x in the table below. The table: x -8,-3,0,3,8 f'(x)-4,-2,0,4,5 If f ′(x) is always increasing, which statement about f(x) must be true? f(x) passes through the origin ...

Which of the following functions grows the fastest as x grows without bound? f(x)=x^2 g(x)=x^2+5x <<<<MY ANSWER h(x)=(sqrt x^4+2x) They all grow at the same rate Compare the growth rate of the functions f(x)=4^x and g(x)=(sqrt 16^x+2^x) f(x) grows faster than g(x) ...

Pre-Calculus 12
Write the following expression as a single logarithm: 4 log 3 + 2

Calculus
Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 2, and x = 1 is revolved around the line y = −2.

Math (Calculus II) (Partial Fraction Decomposition
I'm having trouble trying to solve for the partial fraction decomposition in order to find the integral. ∫ x / (x^4 - a^4) dx I'm assuming a is some constant in this case. So I factored the denominator to this: (x^4 - a^4) = (x^2 + a^2)(x + a)(x - a) Which turns each of them...