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 2x5 − 17

x

x

 

 

 

 

 

Name

MATH 109 – Midterm Exam 1

Section

 

 

 

Spring 2021

1

 

x→0

1 −4

 

 

 

 

 

 

 

 

 

 

 

 

(c) lim

x3 +5x2 +6x

 

 

x→−2 x2 −5x−14

 

2. The function modeling the position d, in meters, of a particle at time t, in seconds, is d(t) = 1 t3 − 2t. Determine

2

 

the velocity of the particle after 3 seconds.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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

(a) (x) = e2+ sin(x2) − √3 x

 

 

 

 

(b) 1 x3 ln x

12

 

 

 

 

 

 

 

 

 

(c) h(t) = −4.9t2 − 20.1− 11

 

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

dx

 

 

(a) x2 + y2 = 16

 

4 20

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(b) sin(y2) + x2 = x

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