# Calculus

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.

Calculus
Given that f(x)=x^3+ax^2+bx has critical points at x=1 and x=5, find a and b and classify the critical points as maxima, minima, or neither.

Pre-calculus
The graph of [r = -5/(2 cos \theta + sin \theta)] is a line. Find the y-intercept of this line.

Pre-calculus
The graph of [r = -5/(2 cos \theta + sin \theta)] is a line. Find the y-intercept of this line.

Calculus
The size of a parcel despatched through the post used to be limited by the fact that the sum of its length and girth (perimeter of the cross section) must not exceed 6 feet. What was the volume of the largest parcel of square cross- section which was acceptable for posting? (...

pre calculus
can you check my work? find two sets of parametric equations for the given rectangular equation x+y^2=4 x=-y^2+4 y=-t^2 x=-t^2+4 x=-t^3 y=-t^3+4 Find a polar equation of an ellipse with its focus at the pole an eccentricity of e=1/4 and directrix at y=4. answer: √(x^2 + y^2...

Calculus AB
The position function of a particle in rectilinear motion is given by s(t) = 2t^3 - 21t^2 + 60t + 3 for t ≥ 0. Find the position and acceleration of the particle at the instant when the particle reverses direction. Include units in your answer. So I've already gotten the ...

Pre-Calculus
The cost of sending a package overnight is $14.40 for the first pound and$3.90 for each additional pound or portion of a pound. A plastic mailing bag can hold up to 3 pounds. The cost f(x) of sending a package in a plastic mailing bag is given by the following function, where...

Calculus
the sum of three positive numbers is 40. The first plus three times the second plus four times the third add up to 80. Select the numbers so that the product of all three is as large as possible.

Calculus
Which would be the best option for finding the limit? lim (1-2x-3x^2)/1+x x->-1 A.Direct substitution B.Dividing out technique C.Rationalization technique D.Indeterminate form

Pre-Calculus
Which of the following shows the correct notation for “The limit of x^2 - 1 as x approaches 3. A. lim x^2-1 x->3 B. lim3 x->x^2-1 C. lim(x^2-3) x->x^2-1 D. lim(x^2-1) x->3 Thank you

Pre-Calculus
What is the correct notation for “The limit of x^2 - 1 as x approaches 3? Thank you

pre-calculus
A rectangular box has a perimeter of 50 inches. Find the length and width of the box that would give the maximum area. Find the maximum possible area of the box.

pre-calculus
A rectangular box has a perimeter of 36 inches. Find the length and width of the box that would give the maximum area. e. l = 9, w = 9 f. l = 81, w = 9 g. l = 27, w = 9 h. l = 18, w = 18

pre-calculus
A rectangular box has a perimeter of 36 inches. Which of the following equations represents the area of the rectangular box in terms of its width, w? a. A = 36w - w2 b. A = 18w - w2 c. A = 36 - w2 d. A = 18 - w2

Calculus
(a) Compute the area of the bounded region enclosed by the curve y = e^x, the line y = 12, and the y-axis. (b) How does this area compare with the value of the integral ∫ from 1 to 12 of (ln x dx)? Explain your answer. (A picture may be helpful.)

Pre-Calculus
How does the expansion of (x + y)n and (x - y)n differ? If you can offer an example that would be very helpful. Thank you

Pre-Calculus
Find first differences for the sequence in order from a_1 to a_5. Determine whether or not the series is quadratic or not.(I used _ as a sign for a subscript) -1, -3, -1, 5, 15 A. 2, 2, 6, 10; not quadratic B. 2, 2, 6, 10; quadratic C. -2, 2, 6, 10; not quadratic D. -2, 2, 6, ...

Calculus
Find the dimensions of the right circular cone of maximum volume having a slant height of 5 ft. See the figure.

Calculus
Find a quadratic model for the sequence. -4, -4, -3, -1, 2 A.y = 0.5x^2 - 0.5x - 4 B.y = 0.5x^2 - 1.5x - 3 C.y = 4.5x^2 - 21.5x+21 D.y = -4.5x^2 + 21.4x - 21

Calculus
Find the second difference for the sequence. 7, 6, 7, 10, 15, 22, …. A.1 B.2 C.3 D.5

Pre-Calculus
Find P_(k+1) if P_(k)=2^(k-1)/k! (I used _ as a sign for a subscript) A. 2^(k+1)/(k+1)! B. 2^k/(k+1)! C. 2^(k+1)/k!+1 D. 2k/k!+1 Thank you

Calculus
If the functions f and g are defined for all real numbers and f is an antiderivative of g, which of the following statements is NOT necessarily true. (A)If g(x)>0 for all x, then f is increasing (B)If g(a)=0, then f(x) has a horizontal tangent at x=a (C)If f(x)=0 for all x...

pre calculus
can you check my work Find two different sets of parametric equations for the given rectangular equation: y=x^2+10 answer: x=t y=t^2+10 x=t^3 y=t^6+10

Calculus
(a) Compute the area of the bounded region enclosed by the curve y = e^x, the line y = 12, and the y-axis. (b) How does this area compare with the value of the integral ∫1-12(ln x dx)? Explain your answer. (A picture may be helpful.)

pre calculus
How would I graph r = cos 5Θ + n cos Θ, 0 ≤ Θ ≤ π For the integers n = -5 to n = 5. ?

Pre-Calculus
Which of the following shows the correct first step to prove the following by mathematical induction? 3 + 11 + 19 + 27 + … + (8n - 5) = n(4n - 1) A. 3 + 11 + 19 + 27 + … + (8 • 1 - 5) = 1(4 • 1 - 1) B. 8 • 1 - 5 = 1(4 • 1 - 1) C. 3 + 11 + 19 + 27 + … + (8k - 5...

Pre-Calculus
Find P + 1 if Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) (the k+1 and k in front of the P are subscripts) A. 7 + 13 + 19 + …+[6(k - 1) + 1] + (6k + 1) + [6(k + 1) + 1] B. 8 + 14 + 20 + …+[7(k - 1) + 1] + (7k + 1) C. 7 + 13 + 19 + …+(6k + 1) D. 7 + 13 + 19 + ...+[6(k...

AP Calculus AB
The fence around Wayne Manor (a rectangular plot of land) is going to be replaced. No fence will be required for the side lying along Gotham river. If the new wrought iron fence costs $12 per meter for the side parallel to the river and$4 per meter for the other two sides, ...

Calculus III
Hi, this question is about Langrange multipliers. Given f(x,y) = y^2 - x^2, subject to the constraint g(x,y) = 0.25x^2 + y^2 = 1, find the max and mins. So I found the partial derivatives for both f(x,y) and g(x,y): fx = -2x fy = 2y gx = 0.5x gy = 2y And set them up for the ...

Calculus
If an isosceles triangle has a fixed perimeter P, find the dimensions that maximize that area. Show how you know that it is the maximum.

calculus
The marginal cost is given by C'(x)=x^(1/3)+9. If the fixed costs are ​\$175​, find the cost of producing 8 units. thank you!!

Math (calculus) (mean values)
A company introduces a new product for which the number of units sold Ss given by the equation below, where t is the time in months. s(t) = 155(7-(9/(2+t))) a) Find he average rate of change of s(t) during the first year. I got the answer to be 1395/28 b) During what month of ...

Calculus III
Hi, this question is about Langrange multipliers. Given f(x,y) = y^2 - x^2, subject to the constraint g(x,y) = 0.25x^2 + y^2 = 1, find the max and mins. So I found the partial derivatives for both f(x,y) and g(x,y): fx = -2x fy = 2y gx = 0.5x gy = 2y And set them up for the ...

Calculus
A trough is 15 ft long and 4 ft across the top. Its ends are isosceles triangles with height 3 ft. Water runs into the trough at the rate of 2.5 ft3/min. How fast is the water level rising when it is 0.89 ft deep? Give your answer correct to 3 decimal places.

Calculus III
Hi, this question is about Langrange multipliers. Given f(x,y) = y^2 - x^2, subject to the constraint g(x,y) = 0.25x^2 + y^2 = 1, find the max and mins. So I found the partial derivatives for both f(x,y) and g(x,y): fx = -2x fy = 2y gx = 0.5x gy = 2y And set them up for the ...

Calculus
a car is traveling along a highway shaped like a parabola with its vertex at the origin. the car starts at 100 miles north and 100 miles west. there is a statue at 100 miles east and 50 miles north. at what point will the cars headlights hit the statue?

Calculus
A car moves along a straight road in such a way that its velocity (in feet per second) at any time t (in seconds) is given by v(t) = 3t * sqrt(49-t^2)

pre calculus
what is the distance between the pole and the directrix of r = 4/-2-6sintheta

Math - Calculus
Find the area of the surface of revolution generated by revolving the curve y = 3 sqrt (x), 0 <= x <= 4, about the x-axis. Okay, so I've set up the integral like this: 2pi ∫[0,4] (3 sqrt (x))(sqrt(1+(1/4x)))dx Which is coming out to 108.5, but that's not giving me the ...

calculus
A paper clip is dropped from the top of a 144‐ft tower, with an initial velocity of 16 ft/sec. Its position function is s(t) = −16t^2 + 144. What is its velocity in ft/sec when it hits the ground? –96 –64 –32 0

calculus
The position function for a particular object is s = â€“23t^2 + 65. Which of the following statements is true? The initial position is 23 The initial velocity is 0 The velocity at time t = 1 is 42 None of these

calculus
Find the local linear approximation of f(x) = e^(3x) at x = 1. y = e^3 y = e^(3(x − 1)) y = 3e^(3)(x − 1) y = 3e^(3)x − 2e^3

calculus
Rolle's theorem cannot be applied to the function f(x) = x^1/3 on the interval [–1, 1] because... f is not differentiable on the interval [–1, 1] f(–1) ≠ f(1) f is not differentiable on the interval [–1, 1] and f(–1) ≠ f(1) Rolle's theorem can be applied to f(x...

calculus
For the function f(x) = 20x^3 − 3x^5, determine the interval(s) for which f(x) increases. (–2, 2) (–∞, –2) U (2, ∞) (–2, 0) U (2, ∞) (–∞, –2) U (0, 2)

calculus
Find limit as x goes to infinity of (6x-(1/4x))/(3x-(1/x))? one half –4 negative one fourth 2

calculus
If the local linear approximation of f(x) = 2cos x + e2x at x = 2 is used to find the approximation for f(2.1), then the % error of this approximation is... greater than 15% between 11% and 15% between 5% and 10% between 0% and 4%

Calculus (vectors)
A plane must travel S15E at 720km/h. If the wind Is from S35W at 130km/h, what heading and airspeed should the pilot set to reach the destination. I got 648km/h E8.89S

calculus
Rolle's theorem cannot be applied to the function f(x) = x1/3 on the interval [–1, 1] because Answer Choices: f is not differentiable on the interval [–1, 1] f(–1) ≠ f(1) f is not differentiable on the interval [–1, 1] and f(–1) ≠ f(1) Rolle's theorem can be ...

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