Mathematics

Mathematics

Problem

Which of the following statements most directly supports the conclusion that lim⁡x→0sin⁡xx=1\displaystyle\lim_{x\to 0}\frac{\sin x}{x}=1? a) For xx near 00, 1≤sin⁡xx≤1cos⁡x1\le \dfrac{\sin x}{x} \le \dfrac{1}{\cos x}, and both endpoint expressions approach 11 as x→0x\to 0. b) For xx near 00, cos⁡x≤sin⁡xx≤1\cos x \le \dfrac{\sin x}{x} \le 1, and lim⁡x→0cos⁡x=1\displaystyle\lim_{x\to 0}\cos x =1. c) For xx near 00, 0<sin⁡xx<10< \dfrac{\sin x}{x} < 1, and lim⁡x→01=1\displaystyle\lim_{x\to 0}1 = 1. d) For xx near 00, sin⁡x<x<tan⁡x\sin x < x < \tan x, and lim⁡x→0sin⁡x=lim⁡x→0tan⁡x=0\displaystyle\lim_{x\to 0}\sin x = \lim_{x\to 0}\tan x =0.

Browse the problem library