# 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.

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.

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

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

(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.