Calculus Answers

1. y= cosh( sin 2/ x squared)
2. [ coth raised to -1 ( sinh(2 raised to 3x))] raised to cube
3. y= x raised to ln (x+2)
4. y= log with base of 4 ( x squared + 3 ) squared square root of 2x -4 / ( x-4 ) raise to 4

1. y = (x+1) (×-2) / (x+1) (x+2)
2. ln xy = 2 raised to x+y
3. y= csc( 2 raised to log with base of 2 x squared)
4. y= arctan ( e raised to x squared 3 raised to x cube)

1. Evaluate lim 1+ e raised to 2x / xcosx
c approaching 0

2. Apply L Hopital's rule to show that lim ( 1+x ) raised to 1/x = e

3. Find dy/ dx and d squared y / d x raised to 2 given x= sinht, y= casht.

4. Approximate the value of arcsin ( 0.48) by differential.

5. The measured radius of the ballbearing is 0.7 inch. If the measurement is correct to within 0.01 inch, estimate the relative error in the volume of the ball bearing.

When a circular plate of metal is heated in an oven, its radius increases at rate of 0.01 cm per minute. At what rate is the plate's area increasing when the radius is 50 cm?

A conical water tank with vertex down has a radius of 10 ft at the top and is 24 ft high. If water flows to the tank at a rate of 20 cube ft per minute, how fast is the depth of the water increasing when the water is 16 ft deep?

Sketch the graph of (x) = 3x raised to 5 - 5x cubeusing calculus based analysis.

What is the smallest perimeter possible for a rectangle whose area is 16 inches?

At what point on the line x=4 does the line segment from (0,0) to(0,6) sibrend the greatest angle?

Find the equations of tangent line and normal lines of parabola y= 2x+ x squared at point (1,3).

Find all the values of x at which the tangent line to the curve y=1/ x + 4 passes through the origin.

QUESTION 1

Use the method of First Principles to find f'(x), given that

f(x) = x^2 + 2x

Find the derivative by differentiation rules/ formulas and simplify awhenever possible.
1. y = (x+1) (×-2) / (x+1) (x+2)
2. ln xy = 2 raised to x+y
3. y= csc( 2 raised to log with base of 2 x squared)
4. y= arctan ( e raised to x squared 3 raised to x cube)
5. y= cosh( sin 2/ x squared)
6. [ coth raised to -1 ( sinh(2 raised to 3x))] raised to cube
7. y= x raised to ln (x+2)
8. y= log with base of 4 ( x squared + 3 ) squared square root of 2x -4 / ( x-4 ) raise to 4

Find the derivative of f(x) = x squared - 4 by definition

y' = lim f( x+h) - f(x) / h
h approaching 0

For what values of a and b is

g(x)= { ax +2b, x is less than and equal to -2 }
{ x squared + 3a- b, -2< x less than and equal to 3 }
{3x-5, x> 3}