# Homework Help: Math: Calculus

## Recent Homework Questions About Calculus

**Calculus (related rates)**

Find dy/dt where y = 2 sqrt(x)-4 and dx/dt = 9 when x = 4.

**Calculus (related rates)**

Find dy/dt when y = 2x2 + 2x + 4 and dx/dt = 14 when x = 7.

**Calculus**

The model for the velocity of a shuttle, from liftoff at t = 0 s until the solid rocket boosters were jettisoned at t = 50.2 s, is given by v(t)=0.001495833t^3−0.089395t^2+18.86t−0.52 (in feet per second). Using this model, estimate the absolute maximum value and ...

**Calculus**

The region in the first quadrant bounded by the x-axis, the line x = π, and the curve y = cos(cos(x)) is rotated about the x-axis. What is the volume of the generated solid? a. 1.921 b. 3.782 c. 6.040 d. 8.130

**Calculus**

The base of a solid in the xy-plane is the circle x^2+y^2 = 16. Cross sections of the solid perpendicular to the y-axis are semicircles. What is the volume, in cubic units, of the solid? a. 128π/3 b. 512π/3 c. 32π/3 d. 2π/3

**Calculus**

If ln(x^2-15y)=x-5+5 and y(-4)=1 find Y prime(-4) by implicit differentiation thus the equation of the tangent line to the graph at the point (-4,1) is y=

**calculus**

If y satisfies y′′ =4, y′(1)=10,and y(1)=6,what is y?

**Calculus - Integrating**

Question: ∫(x^2)/sqrt(x^2+1) u=x^2+1 , x^2= u-1, du=2xdx ∫(u-1)/sqrt(u) , expand ∫u/sqrt(u) - 1/sqrt(u) Integrate: 2/3(u^(3/2)) - 2u^(1/2) + c My answer: [ 2/3(x^2+1)^(3/2) - 2(x^2+1) + c ] When I took the derivative of this to check my answer, it was not (x^2)/sqrt(x^2+...

**Calculus**

An oil tank in the shape of a right circular cylinder, with height 30 meters and a radius of 5 meters is two-thirds full of oil. How much work is required to pump all of the oil over the top of the tank? (The density of oil is 820 kg/m^3 ).

**calculus**

In electrical engineering, a continuous function like f(t)=sin(t), where t is in seconds, is referred to as an analog signal. To digitize the signal, we sample f(t) every ∆t seconds to form the sequence Sn= f(n∆t). For example, sampling f every 1/10 second produces the ...

**Calculus**

What are the dimensions of a rectangular field of area A that requires the least amount of fencing?

**Calculus/Optimisation**

A skateboarded decides to jump off a ramp. The path of the jump from the ramp can be approximated by: h = -3t^2 + 6t + 1 Where h is the height above the ground in meters, s is the horizontal displacement and t is the time after leaving the ramp in seconds. Find the maximum ...

**Calculus/Optimisation**

A real estate manages 80 apartment units. When the rent of each unit is $180 per month, all units are occupied. However, for each $6 increase in rent, one of the units becomes vacant. Each occupied unit requires an average of $18 per month for service and repairs. What rent ...

**Calculus/Optimisation**

An open water tank with a square base is to be made from a thin sheet of metal. find the length of the square base and the height of the tank so that the least amount of metal is used to make a tank of capacity 8 meters cubed

**calculus**

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→∞ {(5x − 4)/(5x + 3)}^5x + 1

**calculus**

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→0 (e^x − e^−x − 2x)/(x − sin(x))

**Integral Calculus**

How to determine the order and degree of this differential equation, (y''')^2-2(y')^6=x-2

**calculus**

Find dy/dx by implicit differentiation. arctan(2x^2y)=x+4xy^2

**pre-Calculus**

find the remainder when (x^40 -3) is divided by (x+1)

**Calculus**

How do you use u-substitution with 20sin(x^2/35)?

**calculus**

find the volume of the unlimited solid obtained by revolving y=1/(x^4 +1) around its asymptote, show work. helllpp pleaseee, I have no idea how to do this...

**calculus**

Find y'and y''. y=x^1/2 ln(x)

**Calculus**

A bowl is created with circular cross sections so that its radius (in cm) is a function of height (in cm) according to the equation r=4sqrt(h+1). Find the volume of soup that fills the bowl if the bow is 2 cm high.

**calculus**

Consider the following function. f(x) = (6 − x)e^−x (c) Find the point of inflection. (If an answer does not exist, enter DNE.) (x,y)=( , )

**calculus**

In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function T(t) = 52 + 15 sin(πt/12) Find the average temperature Tave during the period from 9 AM to 9 PM. (Round your answer to the nearest whole number.)

**calculus**

Consider the given function and the given interval. f(x) = 10 sin(x) − 5 sin(2x), [0, π] (a) Find the average value fave of f on the given interval. (b) Find c such that fave = f(c). (Round your answers to three decimal places.)

**calculus**

A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is 70 ft deep. The bucket is filled with 44 lb of water and is pulled up at a rate of 2 ft/s, but water leaks out of a hole in the bucket at a rate of 0.2 lb/s. Find the work done...

**calculus**

A cable that weighs 6 lb/ft is used to lift 750 lb of coal up a mine shaft 500 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum.

**calculus**

A variable force of 7xâˆ’2 pounds moves an object along a straight line when it is x feet from the origin. Calculate the work done in moving the object from x = 1 ft to x = 19 ft. (Round your answer to two decimal places.)

**calculus**

The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. y = −x2 + 7x − 12, y = 0; about the x-axis

**calculus**

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. y = 4x − x2, y = 3; about x = 1

**calculus**

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. y = x3, y = 8, x = 0; about x = 9

**calculus**

Consider the curve given by the equation ln(y + x + 3) = xy + y3. Find an equation of the tangent line at the point (−4, 2)

**calculus**

Find the centroid (¯ x, ¯ y) of the region bounded by: y = 6x^2+7x, y = 0, x = 0, and x = 7

**calculus**

A circular swimming pool has a diameter of 20 meters, the sides are 3 meters high, and the depth of the water is 2.5 meters. The acceleration due to gravity is 9.8 m/s2 and the density of water is 1000 kg/m3. How much work is required to: (a) pump all of the water over the ...

**Calculus**

Let R be the first quadrant region enclosed by y=e^2, y=e^x and the y-axis. The area of region R is? I don't understand why is the interval is from [0-2]. Thanks

**calculus**

A tank in the shape of an inverted right circular cone has height 10 meters and radius 16 meters. It is ﬁlled with 5 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. Note: the density of hot chocolate is...

**Calculus**

The velocity of an object is given by v(t)=t(t^2-1)^(1/3) feet per second. Find the total number of feet traveled by the object in the time interval [0,3] seconds. I understand how to solve the problem, but I do not understand why is the interval now from [0-1] [1-3], and not ...

**maths/calculus damon,steve,reiny help steve**

x³dy/dx + 3y² = xy² Given x=1 when y=1 plz help me show step help!!

**Calculus - Derivatives**

Use implicit differentiation to find the second derivative y'' of the function given. x^2 + 5y^3 = 8

**Calculus**

Solve the initial value problem. 7x^6-3x^2+5 and u = 1 when x = 1. Is this x^7 - x^3 + 5x - 4?

**Calculus**

Solve the initial value problem. dy/dx = 3 sinx and y = 2 when x = 0. Is this c = 5?

**calculus**

You are visiting your friend Fabio’s house. You ﬁnd that, as a joke, he ﬁlled his swimming pool with Kool-Aid, which dissolved perfectly into the water. However, now that you want to swim, you must remove all of the Kool-Aid contaminated water. The swimming pool is round...

**calculus**

A force of 4 pounds is required to hold a spring stretched 0.1 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.6 feet beyond its natural length?

**Math - Calculus**

Are endpoints also critical points? I'm trying to find the critical points of a function on the interval [-1,5]. So far,the only critical point I have is 2. Does that mean -1 and 5 are also critical points?

**Math Calculus**

Find critical points and extreme values on the interval [-1,5]: f(x)=|x^2-4x+3|

**Math - Calculus**

A piece of wire 16cm long is cut into 2 lengths, one of which is bent into a circle, the other into a rectangle with one side three times the other. a) Determine the ratio of the longer length of the rectangle to the radius of the circle if the sum of the areas of the circle ...

**Calculus**

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 6 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 22 feet high?

**calculus**

A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y=ax^2 about the y-axis. If the dish is to have a 6-foot diameter and a maximum depth of 2 feet, ﬁnd the value of a and the surface area (in square feet) of the dish.

**Calculus Answer Check**

Rocket A has a positive velocity v(t) after being launched upward from an initial height of 0 feet at t=0 seconds. The velocity of the rocket is recorded for certain values of t over the interval 0 <= t <= 80 seconds, as shown below. t(seconds),v(t)(ft/sec) = (0,5),(10,...

**Calculus**

All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the volume changing when each edge is 4 cm? (b) How fast is the volume changing when each edge is 10 cm? Kind of confused... V = x^3 dx/dt = 8 dV/dt = 3x^2 dx/dt (a) When x = 4, ??? (b) ...

**calculus**

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. xy = 2, x = 0, y = 2, y = 4

**Pre-Calculus 12**

Solve the polynomial equation. 2x^3 - 13x^2 + 32x - 13 = 0

**Pre-Calculus 12**

2x^3 - 13x^2 + 32x - 13 = 0

**Calculus**

Solve the inequality |5+(2/x)|<1 solution is (-1/2,-1/3).

**Calculus**

Consider the function on the interval (0, 2π). f(x) = x + 2 sin x relative maximum (x, y) = relative minimum (x, y) = From when I worked out using the first derivative test, I ended up with (2π, 0) for the max and (0,0) for the min. Apparently this isn't correct.

**Calculus**

Consider the differential equation dy/dx = x^2(y - 1). Find the particular solution to this differential equation with initial condition f(0) = 3. I got y = e^(x^3/3) + 2.

**Calculus**

A rectangle trough is 8 meters long, 2 meters across at the top, and 4 meters deep. If water flows in at the rate of 2 cubic meters per minute, how fast is the surface rising when the water is 1 meter deep? Need help on this

**Calculus**

e^(ax) = Ce^(bx) where a does not equal to b and c >0

**Calculus**

Let 5x^2 - 3xy + 58 = 2y^3 Use implicit differentiation to find y' for the above equation. The first thing I did was move 2y^3 over to that everything is equal to 0. With the -3xy I used the product rule and expanded that. After solving I got.... 10x(3 * y + 3x * 1dy/dx)- 6y^...

**Calculus**

Use geometry to evaluate the integral from negative 3 to 3 of f of x, dx for f of x equals the square root of the quantity 4 minus the square of the quantity x plus 1 for x is between negative 3 and 1 including negative 3 and 1, and equals the absolute value of the quantity (x...

**Math/Calculus**

Use the Shell Method to calculate the volume of rotation, V, about the x-axis for the region underneath the graph of y=(x-2)^(1/3)-2 where 10 less than or equal to x which is less than or equal to 218.

**Calculus**

Find the volume of the solid obtained by rotating the region enclosed by the graphs x=y^{5} and x=5sqrty about the y-axis over the interval [0,1].

**Calculus**

Find the volume of the solid whose base is the circle x^2+y^2=64 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal. Find the area of the vertical cross section A at the level x=7.

**calculus**

One leg of a right angle triangle is always 6 meters long, and the other leg is increasing at a rate of 2 meters per second. Find the rate of change of the hypotenuse when it is 10 meters long. plz help

**Calculus AP Exam review explanation pls**

1) The average value of the function g(x) = 3^cos x on the closed interval [ − pi , 0 ] is: 2)The change in the momentum of an object (Δ p) is given by the force, F, acting on the object multiplied by the time interval that the force was acting: Δ p = F Δt . If the force...

**Calculus Antiderivatives**

Find a function whose derivative is a constant k

**calculus**

To ﬁnd the length of the curve deﬁned by y = 5x^3+9x from the point (-3,-162) to the point (1,14), you’d have to compute the integral [a,b] f(x)dx where a = b = f(x) =

**calculus**

A cable hangs between two poles of equal height and 40 feet apart. At a point on the ground directly under the cable and x feet from the point on the ground halfway between the poles the height of the cable in feet is h(x) = 10+(0.1)*(x^1.5). The cable weighs 19.2 pounds per ...

**Calculus**

Consider the differential equation dy/dx = x^4(y - 2). Find the particular solution y = f(x) to the given differential equation with the initial condition f(0) = 0. Is this y=e^(x^5/5)+4?

**Calculus**

Write an expression for y = f(x) by solving the differential equation dy/dx = x√y with the initial condition f(3) = 25. I got y = (x^2/4 + 11/4)^2.

**Calculus AP Exam review explanation pls**

1)What is the area bounded by y = x^2 and y =3x? A)5 B)9/2 ***C)8 D)11.2 E)25 i believe it to be 8 but im not sure. 2)The region R is bounded by the x-axis, x = 2, and y = x^2. Which of these expressions represents the volume of the solid formed by revolving R about the line x...

**calculus**

dt/dx= ((x^2+a^2)^(1/2))/v1+((b^2+d^2)^(1/2))/v1 the function dt/dx has a zero at a unique x on (0,d). Use this to justify your discovery that d= (x^2+a^2)^(1/2) + (b^2+d^2)^(1/2)

**calculus**

find dt/dx t=((a^2+x^2)^1/2)/v1 + ((d^2+b^2)^1/2)/v2

**Pre calculus**

ramp needs an angle of elevation no greater than 4.8. the business has 8 ft to build the ramp. the ramp must rise 6 inches above the ground. can a ramp be built in this space? if a ramp can be built what is the minimum horizontal distance possible? please show work. i'm ...

**Calculus check 1 questiom**

Determine the equation the tangent line on curve 4e^x on (0,4). Since derivative of 4e^x =4e^x, then I plugged in 0 for X and the slope I got was 4. Then I wrote the equation and got y=4x +4

**Calculus**

The position of a particle moving along the x-axis as a function of time,t, is given by x(t)=(1/6)t^3-t^2+3t-1 for t≥0. The particle's velocity becomes three times its initial velocity when t=? I know v(t)=x'(t)=(1/2)t^2-2t+3=9, but I do not understand where does the 9 come ...

**Calculus**

At which point on the curve y = -2+2e^x is the tangent line parrellel to the line 3x-y=5? Just give the x-coordinate as an exact number

**calculus-snell's law**

Suppose A light ray starts at the point A = (0,a) in an uniform medium 1 where the speed of light is c1 and then passes through an uniform medium 2 where the speed of light is c2 reaching point B = (d, −b). The line separating the two media is the x-axis; HINTS ONLY 1) what ...

**calculus**

Find the volume of the solid obtained by rotating the region bounded by the curves y = x^8, y = 1 about the line y = 5.

**calculus**

Find the volume of the solid obtained by rotating the region bounded by the given curves about the speciﬁed axis. x+y = 3, x = 4−(y−1)^2; about the y-axis.

**calculus**

Find the volume of the solid obtained by rotating the region bounded by the given curves about the speciﬁed line. x = 1−y^4, x = 0; about x = 1.

**calculus**

Find the volume of the solid obtained by rotating the region bounded by the given curves about the speciﬁed axis. y = 64x−8x^2, y = 0; about the y-axis.

**calculus I**

Problem: Consider (1) the parabola y=3-1/10 x^2 and (2) the upper half of the circle centered at (20, 0) with radius of 10. Find the points on the parabola where the tangent line is also tangent to the upper half of the circle. (You can find these points in exact form in ...

**calculus**

Find the volume of the solid obtained by rotating the region bounded by the given curves about the speciﬁed line. x = 1−y^4, x = 0; about x = 1.

**Calculus**

The region enclosed by the graph e^(x/2), y=1, and x=ln(3) is revolved around the x-axis. Find the volume of the solid generated. I don't understand if we have to use the washer method or the disk method for this one because when I drew it out on a graph it looked very confusing.

**calculus- optimization**

A rectangle is inscribed into a semi circle at radius 2. What is the largest area it can have and what are the dimensions Answers Area= 4 max base =2sqrt2 height = sqrt2 Help is always appreciated :)

**Calculus**

The region enclosed by the graph e^(x/2), y=1, and x=ln(3) is revolved around the x-axis. Find the volume of the solid generated. I don't understand if we have to use the washer method or the disk method for this one because when I drew it out on a graph it looked very confusing.

**Calculus**

The length l of a rectangle is decreasing at the rate of 3cm/sec, while its width w is increasing at the rate of 3cm/sec. Find the rates of change of the perimeter, and the length of one diagonal at the instant when l=15 and w=6.

**Calculus Reposted**

A point is moving along the curve xy=12. When the point is at (4,3), the x-coordinate decreases at the rate of 2cm/sec. How fast is the y-coordinate changing at that point? dy/dx=-y/x is my change rate so far, should i substitute the coordinates (x,y) to the equation or just ...

**Calculus**

Suppose that the price p, in thousand pesos, and the number of sales x(in hundreds) of a certain item can be modeled by the equation 5p+4x+px=100. Suppose also that the price is increasing at the rate of $200 per year. How fast is the quantity changing at the instant when the ...

**Calculus- Related rates**

A spherical balloon is inflated at the rate of 1 cm^3 per minuter. At the instant when the radius r=1.5, (a.) how fast is the radius increasing? (b.) how fast is the surface area increasing?

**Calculus**

In 1979, a biologist Reto Zach published a study on how crows drop whelks, a type of mollusk, from a height that minimized the amount of energy spent to break open the shells. Drop from too low a height, and the bird has to pick the shell up many times before it breaks. Drop ...

**Calculus**

Quotient Rule: Use the limit definition of the derivative to prove that the quotient rule

**calculus**

it is assumed that f is differentiable and that w has an absolute maximum at t0 w(t)= f(t)/(c+t) derivative is f'(t)(c+t)-f(t)/(c+t)^2 Show that f(t0) = f′(t0)(C + t0). I'm having a bit of trouble in the above question. I keep getting f(t0)= (c+t0)-f'(t0) instead of f(t0) = ...

**Calculus**

A child is flying a kite. If the kite is 135 feet above the child's hand level and the wind is blowing it on a horizontal course at 7 feet per second, the child is paying out cord at ______ feet per second when 285 feet of cord are out. Assume that the cord remains straight ...

**calculus**

w(t)= f(t)/(c+t) w'(t)=? I got f'(t)(c+t)-f(t)/(c+t)^2 as the derivative and I'm having a hard time trying to prove that f(t_0) = f'(t_0) (C+t_0) Help is always appreciated :)

**calculus**

The base of a certain solid is the triangle with vertices at (−6,3), (3,3), and the origin. Cross-sections perpendicular to the y-axis are squares. Then the volume of the solid?

**Calculus**

The graph of the equation is x^2+xy+y^2=9 a) What is the equation of the right most vertical tangent? b) That tangent touches the ellipse where y= what? I've calculated the derivative to y'=(-y-2x)/(2y+x) and I found the horizontal tangents. How do I do this part?

**Calculus**

Consider the given function and the given interval. f(x) = (x − 3)^2, [2, 5] (a) Find the average value fave of f on the given interval. fave = (b) Find c such that fave = f(c). c = (smaller value) c= (larger value)