Math 165: Single Variable Calculus I: Lesson 2 Problems Problems are worth 20 po

Question

Math 165: Single Variable Calculus I: Lesson 2 Problems Problems are worth 20 points each. (1) Guess lim by constructing a table of suitable values using a calculator. (2 Guess lim sin a cos by constructing a table of suitable values using a calculator. (Use radians.) ar 0 1 sin ac cos (3) Guess lima by constructing a table of suitable values using a calculator. sin a sin (4) Guess lim and lim by constructing two tables of suitable values using a calculator r- 0 (5) Sketch a graph of a function y f(a) with domain 0,6] for which the following six limits are correct: f (a) lim lim r 1. (6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Guess lim sin T sin r and lim sin Rinar by constructing two tables of suitable values using a calculator. (Careful: The expression is sin sin r, not sin T sin

Explanation / Answer

lim x->0+ sin x/|x| 1) x = 0.01 ----------------- sin (0.01)/0.01 = 0.999 = 1 2) x = 0.02 ----------------- sin (0.02)/0.02 = 0.99992 = 1 3) x = 0.001 ----------------- sin (0.001)/0.001 = 1 hence lim x->0+ sin x/|x| = 1 lim x->0- sin x/|x| 1) x = -0.01 ----------------- sin (-0.01)/0.01 = -0.999 = -1 2) x = -0.02 ----------------- sin (-0.02)/0.02 = -0.99992 = -1 3) x = -0.001 ----------------- sin (-0.001)/0.001 = -1 hence lim x->0- sin x/|x| = -1 since two limits are different lim x-> 0 sin x / |x| doesnt exist

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