Calculus Help

Name MATH 109 - Midterm Exam 1 Section

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 x→−2

( 12

x+3 − √

23 − x )

(b) lim x→0

2x5− 17x 1 x −4

(c) lim x→−2

x3 +5x2 +6x x2−5x−14

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Name MATH 109 - Midterm Exam 1 Section

2. The function modeling the position d, in meters, of a particle at time t, in seconds, is d(t) = 12 t 3 − 2t. Determine

the velocity of the particle after 3 seconds.

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

(a) f (x) = e2x + sin(x2) − 3 √

x

(b) y = 112 x 3 ln x

(c) h(t) = −4.9t2 − 20.1t − 11

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Name MATH 109 - Midterm Exam 1 Section

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

(a) x 2

4 + y2

20 = 16

(b) sin(y2) + x2 = x

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