# Use implicit differentiation to determine dy for each of the following relations.

**Be sure to show all work for full credit. All answers must be exact values unless otherwise specified. No rough drafts.**

1. Evaluate the following limits. (L’Hopital’s rule is not permitted.) (a) lim (__ 12__ − √23 − *x*)

*x*→−2

*x*+3

(b) lim 2*x*5 − __17__

*x*

*x*

Name

MATH 109 – Midterm Exam 1

Section

Spring 2021

1

*x*→0

1 −4

(c) lim

*x*3 +5*x*2 +6*x*

*x*→−2 *x*2 −5*x*−14

2. The function modeling the position *d*, in meters, of a particle at time *t*, in seconds, is *d*(*t*) = 1 *t*3 − 2*t*. Determine

2

the velocity of the particle after 3 seconds.

3. Determine the derivatives of the following functions. Be mindful of your notation.

(a) *f *(*x*) = *e*2*x *+ sin(*x*2) − √3 *x*

(b) *y *= __1__ *x*3 ln *x*

12

(c) *h*(*t*) = −4.9*t*2 − 20.1*t *− 11

4. Use implicit differentiation to determine * dy *for each of the following relations.

*dx*

(a) *x*2 + *y*2 = 16

4 20

(b) sin(*y*2) + *x*2 = *x*

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