# Show all work and justify all steps, Make sure to fully and clearly...

## Transcribed Text

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 z—HZ— . 2x4 03) (5 MS) 11330 314 _ 1 I2 (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 d 3‘ (5 pts) Find (1—: at (0,0) for ey+y=z2+z+1 4‘ Find Z—y for each of the following Don’t simplify your answer ac z (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: 22+ a (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. Vx2+1 y = e‘(:t + 1)3

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