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A calculus homework problem from math 205, focusing on computing limits of trigonometric functions using limit laws and known limits. The problem includes five questions, each involving the calculation of a limit using the given limits of sin(x)/x and 1 - cos(x)/x.
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Question 1. Compute the following limits using the limit laws and the following two well-known limits: lim x→ 0 sin x x = 1 and lim x→ 0 1 − cos x x
(a) lim x→ 0
sin(3x) 4 x (b) lim x→ 0 x sin(8x)
(c) lim x→ 0 sin(sin x) sin x
(d) lim x→ 0 cos x − 1 sin(3x)
(e) lim x→ 0 tan 2x x
