Math 165 Single Variable Calculus I Lesson 2 Problems Proble

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

Solution

limx--->o sinxcos(1/x) sinx is bounded function as its range is -1 to 1.so x-->0,sinx--->0 therefore=limx-->0sinx*cos(1/x)=0