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 (1 - sin x - cos x )/x 1) x = 0.001 ---------------- lim x->0 (1 - sin (0.001) - cos(0.001))/(0.001) = -0.9995 2) x = 0.002 ---------------- lim x->0 (1 - sin (0.002) - cos(0.002))/(0.002) = -0.998999 3) x = 0.003 ---------------- lim x->0 (1 - sin (0.003) - cos(0.003))/(0.003) = -0.998499 lim x->0 (1 - sin x - cos x )/x = -1

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