# Calculus

**calculus**

Find the domain of the variable x for which the following equation determine y as a real function of x. y - xy = 5

**vector calculus**

Can someone help me with this please. A vector field in cylindrical polar co-ordinates is given by V = R Rˆ + R 3 s i n ( φ ) c o s ( φ ) φˆ + 3 z kˆ where Rˆ, φˆ, kˆ are the appropriate unit vectors. Translate this vector field into the Cartesian x, y, z co-ordinate...

**Applied calculus**

A rectangular plot requires 2000 m of fencing to enclose it. If one of the dimensions is x meters, express the area y (m2) as a function of x. Determine the range of x.

**Calculus**

From each corner of a square of tin, 12 cm on a side, small squares of side x are removed and the edges are turned up to form an open box. Express the volume V (cm3) as a function of x. Determine the range of x.

**Calculus**

Find any critical numbers of the function f(Ø)= 2secØ +tanØ, 10π < Ø < 12π A. 67π/6 B. 71π/6 C. 63π/6 D. A and B

**Calculus**

Find the value of the derivative of the function f(x)=7-|X| at the extrema point (0,7)? A. Does not exist B. 0 C. 7 D. -7

**Calculus**

If f is differentiable at x=c, which of the following statements must be true? A. f is continuous at x=c B. f^1 is continuous at x=c^1 C. f is continuous at y=c D. f is continuous at y^1=c

**Calculus**

A surgical laser is cutting an incision in the eye according to the equation x^2-4y^2=9, y>0. The incision rates vary to allow for curvature of the eye. When x=5, dx/dt=300 manometers per second. What is dy/dt at that moment? A. 18.75 manometers per second B. 93.75 ...

**Calculus**

What is dy/dx given that xy^2-xy+x=y?

**Calculus**

Which of the following is written in explicit form? A.y=x B.x^2-6xy-9y^2=0 C.y=0 D. y= -√1-x^2

**Calculus**

What is the derivative of h(x)= 3x+2/x^2-5?

**Calculus**

What is dy/dx when y=(x^2 - 4x ) ^3 ? A. 3(x^2 -4x)^2 B. (6x - 12) (x^2 -4x)^2 C. 3(2x - 4)^2 D. 6x^2(2x-4)^2

**Calculus**

What is the derivative of k(x)=sin x cos x? A. -sin x cos x B. -2 sin x cos x C. 2 cos^2x-1 D. sin^2x - cos^2x

**Calculus**

If the position function in feet for a free-falling particle on Planet X is s(t)= -8t^2 +16 + 64, what is the velocity of the after 2 seconds in feet per second? A. -32 B. -16 C. 16 D. 64

**Calculus**

From each corner of a square of tin, 12 cm on a side, small squares of side x are removed and the edges are turned up to form an open box. Express the volume V(cm3) as a function of x. Determine the range of x.

**Calculus**

f'(x)=sqrt(x)*sin(x) The first derivative of the function f is given above. If f(0)=0, at which value of x does the function f attain it's minimum value on the closed interval [0,10]? I know the answer is 6.28, but I need steps as to why. Please and thank you.

**PLEASE HELP BEEN STUCK ALL DAY CALCULUS**

The radius of a 12 inch right circular cylinder is measured to be 4 inches, but with a possible error of ±0.2 inch. What is the resulting possible error in the volume of the cylinder? Include units in your answer.

**Calculus Please Help**

The radius of a 12 inch right circular cylinder is measured to be 4 inches, but with a possible error of ±0.2 inch. What is the resulting possible error in the volume of the cylinder? Include units in your answer. my answer 30.16

**Calculus Please Help**

evaluate the table and find d/dx [g[f(2x)]] at x=1 f(x) 6,1,6,2 f'(x) 1,2,5,7 g(x) 1,4,4,3 g'(x) 4,5,5,-4

**Calculus**

Find the x-coordinates where f '(x) = 0 for f(x) = 2x + sin(2x) in the interval [0, 2π]. MY ANSWERS: x = π/2 x = 3π/2

**Calculus**

a 160-inch strip of metal 20 inches wide is to be made into a small open trough by bending up two sides on the long side , at right angles to the base. the sides will be the same height , x. if the tgrough is to have a maximum volume, how many inches should be turned up on ...

**Calculus**

The radius of a 12 inch right circular cylinder is measured to be 4 inches, but with a possible error of ±0.2 inch. What is the resulting possible error in the volume of the cylinder? Include units in your answer. V = πr²h = 16πr² dV/dr = 32πr dV = 16πr dr Let dV and dr...

**Calculus**

The end behavior of f(x)=(2+x^2)/(x^2-36) most closely matches which of the following: y=1 y=-18 y=2 y=0 I still don't get this based on steve's answer will someone please help?

**Calculus**

if f(x)= |(x^2-9)(x^2+1)| how many numbers in the interval [-1,1] satisfy the mean value theorem? None 1 2 3 Will someone please explain in detail?

**Calculus**

A particle moves along the x-axis with position function s(t) = e^cos(x). How many times in the interval [0, 2π] is the velocity equal to 0? 1< My answer 2 3 More than 3 I don't really get this question will someone please explain it to me?

**calculus**

The bending moment (BM) along a beam BM = 30x -5x2 kNm where x is the distance in metres from the left hand end. Find the position and value of the maximum bending moment.

**Calculus**

Can you please help me get the solution to this limit without using squeeze theorem and l'hopitals rule lim x to 0 of x^3 sin(1/x) lim x to 0 of x^2 sin^2(1/x)

**Calculus**

The end behavior of f(x)=(2+x^2)/(x^2-36) most closely matches which of the following: y=1 y=-1 y=2 y=0 There is no leading coefficient so I am not sure what the answer is.

**calculus**

A particle is moving with the given data. Find the position of the particle. a(t) = t2 − 5t + 3, s(0) = 0, s(1) = 20 s(t) =

**pre-Calculus**

Make a conjeture about the symmetry of a) a product of two odd functions b) a product of two even functions c) a product of an odd function and an even function

**AP Calculus**

Ship A is sailing due west at 8km/hr when it sees ship B northwest of its present position. If ship B is sailing due south at 3km/hr, then how close will they come on their courses?

**Pre-Calculus**

Tommy is building a rectangular playpen for his pigs where one side of the play area is a side of his barn. He has enough material to make a fence with a total length of 160 feet. write a función that represents the playpen's área in terms of its length perpendicular to the ...

**Pre-Calculus**

A cylinder's height is 5cm longer than the radias of its base. Write a función modeling the cylinder's volume in terms of its diameter.

**Pre-Calculus**

Squares of side length x are removed from the 4 corners of an 11in by 8.5in piece of paper. The sides are then folded up to create an open-top box. Write a funcion that determines the volume of the box and determine the functions range. How much should be cut from the corners ...

**calculus**

how do I graph this using the first and second derivative and three sign charts. i have to label the inflection point, extreme values and the intercepts also. f(x)= x^3-6x^2

**calculus**

Water leaking onto a floor creates a circular pool with an area that increases at the rate of 3 square inches per minute. How fast is the radius of the pool increasing when the radius is 10 inches?

**Calculus**

What is the largest possible product of two non-negative number whose sum is 1

**calculus**

What is the largest possible product of two negative number whose sum is 1?

**calculus**

is my answer to this question correct A spherical balloon is losing air at the rate of 2 cubic inches per minute. How fast is the radius of the ballon shrinking when the radius is 8 inches. Answer= .0024

**calculus**

Is this the correct answers for these questions Verify the means value theorem holds on the interval shown. Then, find the value c such that f'(c)=(f(b)-f(a))/(b-a) b.f(x)=x^3=x-4 on [-2,3] c= square root 7/3 c. f(x)= x^3 on [-1,2] c= square root 1 d. f(x)= Sqr. root of x on[...

**calculus**

A spherical balloon is losing air at the rate of 2 cubic inches per minute. How fast is the radius of the ballon shrinking when the radius is 8 inches.

**calculus**

Given, F(n+1)-12f(n)=0. n≥1, where F(1)=-3 find the solution to the equation.

**calculus**

find the maximum and minimum value of the function f(x)= x-x^3 on the interval [-2,2] I also need help with this question What is the largest possible product of two negative number whose sum is 1?

**calculus**

Verify the means value theorem holds on the interval shown. Then, find the value c such that f'(c)=(f(b)-f(a))/(b-a) a. f(x)= x-1/x on [1,3] b.f(x)=x^3=x-4 on [-2,3] c. f(x)= x^3 on [-1,2] d. f(x)= Sqr. root of x on [0,4]

**More calculus**

A garden is to be designed in the shape of a circular sector, with radius r and central angle theta. the garden is to have a fixed area A. for what value of R and theta will the length of the fencing be minimized?

**Calculus**

Find all values of a, B so that the function f(x)=1 if x>3, f(x)=ax-10 if x<3, and f(x)=B otherwise is continuous everywhere. I think a is continuous everywhere since ax-10 is a polynomial, and b is continuous at x=3.

**Calculus**

use implicit differentiation to find dy/dx if 5xy+x^2y=10 Is this correct answer for this question (-5y-2xy)/(12x)

**calculus**

find the equation of the tangent line to the graph of -x^2+2y^2+3x=-2 at the points with x-coordinates x=4

**calculus**

use implicit differentiation to find dy/dx if 5xy+x^2y=10

**calculus**

Use the definition of derivative: lim(as h approaches 0) (f(x+h)-f(x)/(h) to find f(x)=(1)/(2x).

**calculus**

f'(-2) if f(x)= g(h(x))^3 Chart x= -3,-2,-1,0,1,2,3 g(x)= 0,1,3,2,0,-2,-3 h(x)= 1,2,0,3,-1,-2,0 g'(x)= 1,2,-1,-2,-2,-1,0 h'(x)= 0,-3,-2,3,-2,0,1

**Calculus**

Find f'(1) if f(x)=(h(x))^3 Chart: x= -3,-2,-1,0,1,2,3 g(x)= 0,1,3,2,0,-2,-3 h(x)= 1,2,0,3,-1,-2,0 g'(x)= 1,2,-1,-2,-2,-1,0 h'(x)= 0,-3,-2,3,-2,0,1

**calculus**

f'(-2) if F(x)=g(h(x))

**Calculus**

How do you find the total distance a particle travels on a given interval on a graph and net distance?

**Calculus**

Water is drained out of tank, shaped as an inverted right circular cone that has a radius of 6cm and a height of 12cm, at the rate of 3 cm3/min. At what rate is the depth of the water changing at the instant when the water in the tank is 9 cm deep? Give an exact answer showing...

**calculus**

how do i get the answer for this limit limit x to 0 (4^2x-1) without using direct substitution my work so far is limit x to 0= (4^2x-1) = (4^2x/4^-1) is it correct?

**Calculus**

Two horizontal forces, and , are acting on a box, but only is shown in the drawing. can point either to the right or to the left. The box moves only along the x axis. There is no friction between the box and the surface. Suppose that = +4.2 N and the mass of the ...

**math - calculus help!**

An inverted conical tank (with vertex down) is 14 feet across the top and 24 feet deep. If water is flowing in at a rate of 12 ft3/min, find the rate of change of the depth of the water when the water is 10 feet deep. 0.229 ft/min 0.449 ft/min 0.669 ft/min 0.778 ft/min 44.90 ...

**integral calculus**

integrate: [ cos ^ 2 (x) * sin (x) / ( 1 - sin(x) )] - sin (x)

**integral calculus**

Integrate (((cos^2(x)*sin(x)/(1-sin(x)))-sin(x))dx thanks

**calculus-add**

(2y-1)dy/dx=(3x^2+1) given that x=1 when y=2 plz show step thanks 2) (a)find the general solution of the equation (x-2)dy/dx+3y(x-1)/(x+1)=1 b)given the boundary condition y=5 when x=-1,find the particular solution of the condition given in (a) a little help would do thanks i ...

**calculus**

(2y-1)dy/dx=(3x^2+1) given that x=1 when y=2 plz show step thanks

**integral calculus**

integral of (dx/(coth^2(2x)*sinh^2(2x)) help, thanksss

**calculus help**

the bend moment M of a beam is given by dm/dx=-w(1-x) where w and l are constants.determine M in terms of x given that M=wl^2/2 plz show me working step

**Calculus**

How do I find the limit of x/x as x approaches 0?

**calculus**

solve for dy/dx=(x^2+y^2)/xy by substitution. Plz help step

**Calculus**

The Question: A particle moves along the X-axis so that at time t > or equal to 0 its position is given by x(t) = cos(√t). What is the velocity of the particle at the first instance the particle is at the origin? So far I was able to determine that the velocity of the ...

**calculus help me plz too hard show step**

charge Q coulombs at time t seconds is given by the differential equation RdQ/dt+Q/C=0, where c is the capacitance in farafd and R the resistance in ohms.solve the equation for Q given that Q=Qo where t=0 plz show step plz plz plz

**calculus too hard**

the velocity of a chemical reaction is given by dx/dx=k(a-x) where x is the amount transfered in time t,k is a constant and a is the condition at time t=0 when c=0 solve the equation and determine x in terms of t? Plz show work plz plz

**Calculus 3**

F(x, y) represents a velocity field of a fluid over a surface S defined by z = 6 − 3x − 2y. If the magnitude of the velocity in the direction of the unit normal vector, n̂, on S is 3z⁄√14, compute the flux of F(x, y) over the surface S in the first octant oriented ...

**Calculus**

If y = 2x - 8, find the minimum value of the product of xy. I think this is -8.

**calculus**

when a circular plate of metal is heated in an oven, its radius increases at the rate of 0.01 cm/min. At what rate is the plate's area increasing when the radius is 60 cm?

**calculus**

A 13 foot ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft. from the house, the base is moving at the rate of 10ft./s. How fast is the top of the ladder sliding down the wall then?

**calculus**

A Veterinarian has 80 feet of fence and he wants to enclose a rectangular dog-run along the back side of his office building. He will not fence the side along the building. What are the dimensions of the dog-run that give the maximum area he desires?

**calculus**

Jen needs to make a flyer for her dog's birthday party. She wants the flyer to contain 40 square inches of printed portion and she wants to use 1 inch of each side as well as 2 inches of top and bottom of the paper for decoration. What size paper should Jen choose in order to ...

**calculus**

find the location and values of any global extrema of F(x)= x^3-3x^2-9x on the interval [-2,4] (you must show your work by finding critical points

**calculus**

Find two numbers whose product is 16 and whose sum of squares is minimum

**calculus**

f(x)=−x3 −x2 +16x+16 1. Calculate f′(x). 2. Calculate f′′(x). 3. Find the x values such that f(x) = 0. Note: this can be done by factoring. 4. Find the stationary point/s. Note: a point requires x and y coordinates. 5. Determine the nature of this/these point/s. 6. ...

**Pre- calculus**

Change the equation to rectangular coordinates: r= 2(sin theta-cos theta)

**pre calculus**

change the equation to rectangular coordinates: r= 2(sin theta -cos theta)

**Pre calculus**

in the equation r= 5/(sin theta +2cos theta) the letters r and theta represent polar coordinates. Write the equivalent equation using rectangular coordinates. Thanks :)

**pre calculus**

in the equation (x-4)^2+y^2=16 the letters x and y represent rectangular coordinates. Write the equivalent equation using polar coordinates. solve for r

**Calculus**

A chemical substance is draining from a conical filtering system at a rate of 100 cubic centimeters per minute into a cylindrical storage tank below. The conical filter and cylindrical tank each have a diameter of 60 centimeters, and the height of the cone also measures 60 ...

**Calculus**

The horizontal position of an object from a point of origin in meters is modeled by the function x(t)= (1+sin(t))/(2+cos(t)) where t is measured in minutes and 0 is less than or equal to t which is less than or equal to 5. A) show that x(t)= (2cos(t)+sin (t)+1)/(2+cos(t))^2 B...

**Calculus Help 3 Questions**

3.The position (feet traveled) of a car is given by the equation s(t)= 4t2 + 4t. Find the time when the car is going the same speed as its average speed over the interval 0 to 10 seconds. A)t=0 B)t=2.5 C)t=5 D)t=10 E)Never 4. Consider the curve given by x2 + sin(xy) + 3y2 = C...

**Calculus**

Please help me. 1. Use the definition of the derivative to find f'(x), if f(x)=x^-2 2.Find the derivative of y=3t^5 - 5√t + 7/t

**Calculus**

A light on the ground moving at 0.5 m/s approaches a man standing 4 m from a wall. How fast is the tip of the man’s shadow moving when the light is 10 m from the wall?

**Math, calculus, advanced functions, pre calculus**

An investments value, V(t) is modelled by the function V(t)=2500(1.15)^2, where t is the number of years after funds are invested A) find the instantaneous rate of change in the value of the investment at t=4, what intervals would you choose? Why? My question is ... Which ...

**calculus**

find the area of the region bounded by the curves f(x)=x-x^3 ; g(x)=x^2-x ; over [0,1]

**Calculus Finals Review sheet!! Explanation needed**

Here is a graph of the derivative y' of a continuous, differentiable function. For approximately what values of x between Ã¢Ë†â€™5 and 5 does the original function y have inflection points? Find limit as x approaches 3.5 [[x-2]]/x (Remember that [[x]] is the greatest...

**calculus**

hey can someone help me with these i need help Consider the curve given by x2 + sin(xy) + 3y2 = C, where C is a constant. The point (1, 1) lies on this curve. Use the tangent line approximation to approximate the y-coordinate when x = 1.01. Question 19 options: 0.996 1 1.004 ...

**calculus**

can you guys help me with these questions Which of the following could be the units for dy/dx if y is the surface area of a tumor and x is the radius of the tumor? square millimeters per millimeter millimeters per centimeter meters per second gallons per hour meters per radian...

**Calculus!! HELP!!**

1) The sides of the triangle shown increase in such a way that (dz/dt=1) and (dx/dt=(3dy/dx)) At the instant when x = 12 and y = 5, what is the value of dx/dt? 2) Let f(x) = x^3 − 4. Which of these is the equation for the normal line to this curve at the point (2,4). A) y=1/...

**Calculus**

The cost of producing commodity is C(X)=3X^2+4X+8 dollars.If the price is P(X)=(50-X) dollars per unit,determine the level of production that maximizes the profit. ---------- What is the level of production.

**Calculus**

A car traveling 96ft/s begins a negative acceleration at a constant rate of 12ft/s^2. After how many seconds does the car come to a stop? How far will the car have traveled before stopping? Anti-derivatives are involved somewhere in the 2nd part I believe.

**calculus!**

use the definition of derivative to find d/dx(1/(3-x))

**calculus**

use implicit differentiation to show: d/dx(tan^-1x)=1/(x^2+1)

**calculus**

If you are blowing up a balloon at a rate of 3 cubic ft per min, what is the rate of change of the radius after 30 seconds

**calculus**

A rectangle has an area of A. Find the dimensions that minimize the perimeter. Show that it really is a minimum.

**Calculus**

Determine the open intervals on which the graph of f(x) = -7x^2 + 8x + 1 is concave downward or concave upward. The second derivative is just -14, so I don't know what to do with that.