Homework Help for Calculus

Differentiate x tan x.

2. Solve the following DE using an Substitution:

(X³ +y³) dx+ 3xy² dy=0, y(0)=4

∫ 6y2 + 12y .dy =  6 ∫ y2 + 2y .dy    

The minute hand on a clock is 10 mm long and the hour hand is 7 mm long. How fast is the distance between the tips of the hands changing at 6:45?

Please show all work and explain. Thanks.

A CAT scan produces equally spaced cross-sectional views of a human organ that provide information about the organ otherwise obtained only by surgery. Suppose that a CAT scan of a human liver shows cross-sections spaced 1.5 cm apart. The liver is 15 cm long and the cross-sectional areas, in square centimeters, are 0, 19, 59, 77, 94, 106, 118, 128, 64, 38, and 0. Use the Midpoint Rule with n=5n=5 to estimate the volume VV of the liver.

Question 13

In Suburb 1, the number of doctors t years after 2000 can be modeled using , while the number of nurses can be modeled using .

Aitana can express the ratio of doctors to nurses in Suburb 1 of Las Vegas as _______________. (You do not need to simplify your answer. Remember the ratio of A to B is the quotient ).

Derivative of 4X^2+sqrt(x)^4

The period T of a pendulum of length L is given by  where g is the acceleration due to gravity. A pendulum is moved from the Canal Zone, where g = 32.09 feet per second per second, to Greenland, where g = 32.24 feet per second per second. Because of the change in temperature, the length of the pendulum changes from 2.5 feet to 2.48 feet. Approximate the change in the period of the pendulum.

Consider the equation below: 20x^2 − y + 4z^2 = 0

Reduce the equation to one of the standard forms

Sketch the surface.

Write an equation for the cross section at:

z = 0 using x and y

y = −2 using x and z

y = -2 using x and z

x = 0 using y and z

Finding the second derivative:

 The graph of y = is shown below. Use it to answer the following questions. 

Remember this is the graph of y =

Please help with this question for calculus involving interval notation and x values with min and maximum values.

(1 point) Suppose that f(x)=(x+2)(x−2)2.

(A) Find all critical values of f. If there are no critical values, enter -1000. If there are more than one, enter them separated by commas.
Critical value(s) =

(B) Use the second derivative test to find the x-coordinates of all local maxima of f. If there are no local maxima, enter -1000. If there are more than one, enter them separated by commas.

Local maxima at x =

(C) Use the second derivative test to find the x-coordinates of all local minima of f. If there are no local minima, enter -1000. If there are more than one, enter them separated by commas.

Local minima at x =

Please help with this calculus question involving intervals, min and maximums. The problem is f(x) 6x + (6/x)

(1 point) Let f(x) = 6x + 6x.

(A) Use interval notation to indicate where f(x) is increasing.
Note: Use 'INF' for ∞, '-INF' for −∞, and use 'U' for the union symbol. Increasing:

(B) Use interval notation to indicate where f(x) is decreasing. Decreasing:

(C) List the x values of all local maxima of f. If there are no local maxima, enter 'NONE'. x values of local maximums =

(D) List the x values of all local minima of f. If there are no local minima, enter 'NONE'. x values of local minimums =