Calculus Answers

prove that f(x)= | x+1| has no tangent line at (-1 0)

Find the volume of the solid formed by the region bounded by the functions

y = 6 - 2x - x^2, y = x + 6

Using L'Hospital's Rule to determine limits to infinity

Differentiation. Find the derivative of the given function. Use quotient rule.

f(x)= (x^-1)/(x+x^-1)

Suppose that in t hours, a truck travels s(t) miles, where s(t)= 10t² . Find the average rate of change of distance with respect to time from t1 = 2 and t2 = 5.

The volume of a cube is increasing at a rate of 1200 cm3/min at the

moment the lengths of the sides are 20 cm. How fast are the lengths of

the sides increasing at that moment?

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1. Let f be the function defined by

f (x) = x2

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(2x + 1)2

:

(a) Determine the vertical and horizontal asymptotes (show all limits). (4)

(b) Use the sign pattern for f ' (x) to determine

(i) the interval(s) over which f rises and where it falls; (4)

(ii) the local extrema. (2)

(c) Use the sign pattern for f " (x) to determine

(i) where the graph of f is concave up and where it is concave down. (4)

(ii) the inflection points (if any) (2)

Find the area of the surface generated by revolving the curve y=√25-x², from x = - 2 to x = 3 , about the x-axis.

Find the length of the arc with the curve

y = 2x ^ (3/2) between x = 1/3 and x = 7