Originally Posted by

**neilbachman** so i somehow managed to get into business calculus in school and i'm sure these questions are easy for most but can u help.

Directions: Find the rate of change of the given function f(x) with respect to x for the prescribed value x=c

Question: f(x) = x- square root of x + 1/x^2 ; x=1

$\displaystyle \textcolor{red}{f(x) = x - x^{\frac{1}{2}} + x^{-2}}$

use the power rule for derivatives to find f'(x), then evaluate f'(1)

2. the manager of the many facets jewelry store models total sales by the function s(t)= 2,000t/(4 + 0.3t) where t is the time (years) since the year 2000 and s is measured in thousands of dollars.

a. At what rate are sales changing in the year 2002

use the quotient rule to find s'(t), then evaluate s'(2)

b. what happens to sales in the "long run" (that is as t--> + infinity

what is the value for the horizontal asymptote for s(t) ?

3. an efficency study of the morning shift at a certain factory indicates that an average worker arriving on the job at 8:00 A.M. will have produced Q(t) = -t^3 + 8t^2 + 15t units t hours later.

a. compute the workers rate of production **R(t) = Q(t)** ???

should be R(t) = Q'(t). use the power rule to calculate Q'(t)

b. at what rate is the workers rate of production changing with respect to time at 9:00 A.M.

evaluate R'(1) = Q''(1)

4. Find the Limits

lim 5-2x^3/

x-->infinity x^2 +1

does not exist since degree of the numerator > degree of the denominator

5. lim 2x^2 + x - 6/ 4x^2 -4x -3

x-->3/2

factor numerator and denominator, cancel any common factors, then evaluate the limit at x = 3/2