Calculus Answers

Find the most general antiderivative of the function. Use C for any needed constant. (Check your answer by differentiation.) (x>0)
g(x) = (6 - 4 x^3 + 3 x^(7))/x^(7)

G(x)=

Evaluate the limit. (If you need to use -infinity or infinity, enter -INFINITY or INFINITY.)

lim x->0 (e^x-e^-x-2x)/(x-sin(x))

Evaluate the limit.

lim x->0^+ (9x+1)^cot(x)

Evaluate the limit. (If you need to use -infinity or infinity, enter -INFINITY or INFINITY.)

limit x->1( (5x/x-1) -(5/ln(x))

Differentiate the function.

y= e^(k tan(sqrt(7 x)))

y'(x) =

Find h'(1) given that f(1) = -5, f '(1) = 2, g(1) = 3, and g'(1) = 2

h(x) = f(x)/g(x)

h'(1) =

Use the definition of e, and numerical approximations as y approaches 0 from the left, and y approaches 0 from the right.

(b) Use a calculator to estimate the values of the limits given below, correct to two decimal places.
lim (y -> 0) (2.7[sup]y[/sup] - 1)/ y and lim (y -> 0) (2.8[sup]y[/sup] - 1)/ y

____ < 1 < _______

What can you conclude about the value of e?

________ < e < _________

Find
Lim x --->∞ ln(x)/x^4

A piece of wire 25 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (Give your answers correct to two decimal places.)

(a) How much wire should be used for the square in order to maximize the total area?


(b) How much wire should be used for the square in order to minimize the total area?

From the graph of f(x)=3x^4-20x^3+24x^2, identify on the interval [-1,5] the x-y coordinates of the absolute maximum.

Give your answer in the form (a,b). If there is more than one answer enter points separated by commas. For example (a,b), (c,d)