Show all work and justify all steps, Make sure to fully and clearly answer each question,
1, Evaluate the following limits
(a) (5 pts) lim I
03) (5 MS) 11330 314 _ 1
(0) (5 pts) lim 7
z—m 1n 1'
(d) (5 pts) allinéxlnlxl
2. (5 pts) Find f’ (5) using the limit deﬁnition of the derivative, for f(ar) = x/a: — 1
3‘ (5 pts) Find (1—: at (0,0) for
4‘ Find Z—y for each of the following Don’t simplify your answer
(a) (spts) y= g
(b) (3 PtS) y = cos (x — 9:2)
5. Use the function to solve each part: f (z) = $3 — 3x + 1
(a) (3 pts) Find any mlative extrema of f, or explain why none can be found.
(b) (3 pts) Find the maximum and minimum of f on [0, 2], if either exists.
(c) (3 pts) Determine the intervals on which f is concave up
6, (5 pts) Use linearization to approximate W
7, Evaluate the following integrals:
(a) (5 pts) / Z 1d:
(b) (5 pts) A (12 + 1) dz
8, (7 pts) A rectangular corral is going to be built to enclose 20000 f 152 total space, divided into
two equally sized rectangular sections. What’s the least amount of fencing needed to build a
corral to those speciﬁcations?
. . . . . . d . .
9. (5 pts) Use logarithmic differentiation to determine 35 for the followmg.
y = e‘(:t + 1)3
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