# Calculus

Calculus
For a cylinder with a surface area of 20 20, what is the maximum volume that it can have? Round your answer to the nearest 4 decimal places.

Calculus
A rectangular box has a square base. If the sum of the height and the perimeter of the square base is 14 in, what is the maximum possible volume?

The limit limh->0 ((sqrt1+h)-1)/h represents the derivative of some function f(x) at some number a. Find f and a. Please help!

Pre calculus
Write a polynomial function given the zeroes: 11i and -11i

Calculus
A dog kennel with four pens is to be constructed. The pens will be surrounded by rectangular fence that costs \$13 per meter. The rectangle is partioned into four pens of equal size with three partitions made of fence that costs \$5 per meter. Each pen measures x meters wide by ...

calculus
Consider the series ∑ ∞ n=1 (13/10^n) Determine whether the series converges, and if it converges, determine its value. Converges (y/n):

Pre-calculus
Parabola x^2+10x+4y29=0 in standard form

Calculus - Newton's Method
Use the Newton's Method to approximate the real root of the equation: f(x)=x-2+cosx=0 a) What is the iterative equation of Newton's method of the given equation? b) Iterate the equation with starting point x1=5 until you get a repetition of the four digits after the decimal ...

calculus
evaluate the integral. from 0 to 4π t^2 sin(2t) dt

Calculus
Find the inflection points and where the function is concave up and concave down: f(x)=x/(x+x^2)

calculus
(ln(x))^2 dx, integrate.

Calculus
Let f(x)=αx^2+βx+γ be a quadratic function, so α≠0, and let I=[a,b]. a) Check f satisfies the hypothesis of the Mean Value Theorem. b)Show that the number c ∈ (a,b) in the Mean Value Theorem is the midpoint of the interval I.

Math - Calculus
You are given 1200 cm^2 of cardboard to make a box with a square base and an open top. Find the largest possible volume of the box.

calculus
Equilateral hexagon is revolving around one of its edges. Find the volume of the solid of revolution. no idea how to do this can someone please help!!! urgent!

1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but do not evaluate, the integral which gives the volume when the ...

Calculus
What is the function y (x) if it statisfies Y"=6 y'(1)=4 and y (1)=6

Math -- Calculus
Some years from now you are working for a book publisher. Your boss asks you to give him a formula that will tell him the length and width of a book page that contains A square inches of printed text, a left margin of L inches, a right margin of R inches, a top margin of T ...

Calculus
A tank contains 100 grams of a substance dissolved in a large amount of water. The tank is filtered in such a way that water drains from the tank, leaving the substance behind in the tank. Consider the volume of the dissolved substance to be negligible. At what rate is the ...

Calculus - Optomization Problem
The volume of the largest right circular cone that you can inscribe in a sphere of radius r equals _______ (Your answer will be an expression in r.)

Calculus
A boat is pulled in to a dock by a rope with one end attached to the front of the boat and the other end passing through a ring attached to the dock at a point 6 ft higher than the front of the boat. The rope is being pulled through the ring at the rate of 0.2 ft/sec. How fast...

Calculus
A tank contains 100 grams of a substance dissolved in a large amount of water. The tank is filtered in such a way that water drains from the tank, leaving the substance behind in the tank. Consider the volume of the dissolved substance to be negligible. At what rate is the ...

Calculus
Find dy/dt where y = 2 sqrt(2)− 4 and dx/dt = 9 when x = 4. I found the derivative of y=2sqrt(2)-4 but I am stuck as to where to plug in dx/dt

Calculus help
You are going to make many cylindrical cans. The cans will hold different volumes. But you'd like them all to be such that the amount of sheet metal used for the cans is as small as possible, subject to the can holding the specific volume. How do you choose the ratio of ...

Calculus (related rates)
A ladder 13 meters long rests on horizontal ground and leans against a vertical wall. The foot of the ladder is pulled away from the wall at the rate of 0.4 m/sec. How fast is the top sliding down the wall when the foot of the ladder is 5 m from the wall?

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.

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))/v​1 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