Spring 19 Test 1 Practice This is a practice test only, do not expect the test to look exactly like this. Problem 1. (a) What are the two possible definitions for f'(a) (hint: both are limits, one uses x - a and the other h - 0)? (b) Find f'(1), where f(x) = v3 + x2, using the definition of your choice from part (a). Problem 2. Find the slant asymptote of 42 025 - 32-2022 2 - 2022 + 2 2021 Problem 3. Evaluate the following limits algebraically, showing all work. If the limit does not exist, then write DNE and explain why it does not exist. (a) lim 2x2 + 3x + 1 x-+00 12 + 2x + 1 (b) lim 2x2 + 3x + 1 T- 2 2 + 2x + 1 pinu a doidw sol levasini the onionsded .S (c) lim 2x2 + 3x + 1 VI odd ovlol .adai * +- 1+ x2 + 2x+ 1 (d) lim 2 2 + 9 - 5 It ( 800) 2 4 - 4 x + 4 e) lim 2+ 3x2 1 +0 4x - 1 f) lim arctan I + 2 - Problem 4. The following table shows the population P over t months for a rare breed of fish with no eyes (called a fsh) which scientists found deep in a cave. t (months) 0 2 4 6 8 10 12 2 P (population of fsh) 77 78 74 63 58 53 50 (a) Estimate P'(10) and explain/interpret what it means. (b) Use your estimate from the previous part to find the equation of the tangent line to P(t) at t = 10. Problem 5. of e in the following function continuous on (-oo, oo)? (a) State the Squeeze Theorem. (b) Use the Squeeze Theorem find lim ((x - 4)? f(x)) if x