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
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
b. what happens to sales in the "long run" (that is as t--> + infinity
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)
b. at what rate is the workers rate of production changing with respect to time at 9:00 A.M.
4. Find the Limits
x-->infinity x^2 +1
5. lim 2x^2 + x - 6/ 4x^2 -4x -3
thanks for any help u can give.