# Calculus

**Calculus**

Show that volume of the solid generated by revolving y=1/x between x=1,2x=infinity about x-axis

**Calculus**

Find the length of the parabola y^2=4ax cut off the line x=a about the x-axis

**Calculus**

The marginal cost for producing x units of a certain product is given by the formula MC = 0.001x^2-0.5x+66.5. A. What is the increase in the cost of the production if the production level is raised from 200 to 400 units? B. What is the average cost per item of producing 330 ...

**pre-calculus**

how to find the equation of a parabola given foci(-7,-17), (-7,17 ),the absolute value of the difference of the distances of any point from the foci is 24

**Calculus II**

Find the derivative of 5^(x^3+x) I know the answer, it's: 5^(x^3+x)*ln(5)*(3x^2+ 1) I just need some help on how to derive that. What rule is at work here? where did the ln come from?

**calculus**

Use x=-1/2 in the MacLaurin series for e^x to approximate 1/sqrt (e) to four decimal places. So far I have |f^n(0)/n! (1/sqrt(e)-1/2)^n)| </= 1/10^4, but I don't know what to do from here.

**calculus**

Find the length of the curve given by the equation y= intergral from -pi to x of sqrt(cos(t)) dt for x between -pi and pi. I think I know to do this- at least part of it. I am using the fundamental theorem of calculus and the arc length formula, but I don't know how to find ...

**Calculus**

Hi, I am trying to find a closed form for the power series from n=2 to infinity of x^n/(n-1)n. I'm not really sure how to do this- I found the first and second derivatives which were x^(n-1)/(n-1) and x^n-2. However, this didnt really seem to help much. Any help is appreciated!

**calculus**

Use x=-1/2 in the MacLaurin series for e^x to approximate 1/sqrt (e) to four decimal places. So far I have |f^n(0)/n! (1/sqrt(e)-1/2)^n)| </= 1/10^4, but I don't know what to do from here.

**calculus**

Use x=-1/2 in the MacLaurin series for e^x to approximate 1/sqrt (e) to four decimal places. So far I have |f^n(0)/n! (1/sqrt(e)-1/2)^n)| </= 1/10^4, but I don't know what to do from here.

**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)

**calculus help pls**

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? These are the choices: 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.

**Please help Calculus**

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.

**Calculus Please Help**

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

**Calculus Please Check my answer**

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...

**Calculus Please Check my answer**

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 ...