Question

Evaluate lim theta→0 sin 7 theta/theta​

Answer 1

Answer:

see the attached document

Answer 2

$lim_{\theta \rightarrow 0} \ \frac{sin 7 \theta}{\theta}$ = 7

Step-by-step explanation:

Given: Mathematical expression $lim_{\theta \rightarrow 0} \ \frac{sin 7 \theta}{\theta}$

To Find: Evaluate the given expression

Solution:

• Evaluating $lim_{\theta \rightarrow 0} \ \frac{sin 7 \theta}{\theta}$

$\Rightarrow lim_{\theta \rightarrow 0} \ \frac{sin 7 \theta}{\theta}$

on dividing and multiplying by 7, we get,

$\Rightarrow lim_{\theta \rightarrow 0} \ \frac{sin 7 \theta}{7 \theta} \times 7$

Since $lim_{x \rightarrow 0} \ \frac{sin x}{x} = 1$, therefore,

$\Rightarrow lim_{\theta \rightarrow 0} \ \frac{sin 7 \theta}{7 \theta} \times 7 = (1) \times 7 = 7$

Hence, $lim_{\theta \rightarrow 0} \ \frac{sin 7 \theta}{\theta} = 7$