Question

Limit x tend to 0 sin5x by tan7x

Answer 1

$\bold{Lim_{x\to 0} \,\frac{sin5x}{tan7x}}$
First of all we should check form of limit ,
put x = 0 we get 0/0 it is in the form of limit .

Now, we should apply standard form of limit and its solution.
e.g., $\bold{Lim_{x\to 0} \,\frac{sinx}{x}}=1$
and similarly , $\bold{Lim_{x\to 0} \,\frac{tanx}{x}}=1$
Use these here,

$\bold{Lim_{x\to 0} \,\frac{(sin5x).5x.(7x)}{(5x).tan7x(7x)}}$
$\bold{Lim_{x\to 0} \,\frac{sin5x}{5x}.\frac{7x}{tan7x}.\frac{5x}{7x}}}$
$\bold{Lim_{x\to 0} \,\frac{5x}{7x}}}$
= 5/7

Hence, answer is 5/7