Math 165: Single Variable Calculus I: Lesson 2 Problems Problems are worth 20 po
ID: 3117908 • Letter: M
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 sinExplanation / Answer
lim x->0 sin x cos 1/x 1) x=0.001 --------------- sin (0.001) cos(1/0.001) = 0.000562379 2) x=0.002 --------------- sin (0.002) cos(1/0.002) = -0.0017677 3) x=0.003 --------------- sin (0.003) cos(1/0.003) = 0.00284341 hence, lim x->0 sin x cos 1/x = 0