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[tex]\lim_{x\rightarrow} \frac{\sin x}{x} = 1 [/tex]

Solution

Given [tex] \epsilon > 0 [/tex]

want to find [tex]\delta [/tex] such that [tex]\left|\frac{\sin x}{x} - 1 \right| < \epsilon [/tex]

for x, [tex] |x | < \delta [/tex]

can I use Taylor expansion of sinx ? but Taylor is an approximation of sin(x) around a certain point ? how to find such a delta ?

Thanks