Question

What is the value of the limit with step by step solution?

Answer 1

the answer is 1
the general formula is lim(x--->0) sinx/x=1
here 1/x tends to 0 when x tends to infinity and thus it is basically the formula which is applied

Answer 2

$\lim_{x \to \infty} \frac {sin\frac {1}{x}}{\frac {1}{x}}$
Put x⇒∞ then we see limit is in the form of 0/0
Now use the concept of L-Hospital rule ,
$\lim_{x \to \infty} \frac {sin\frac {1}{x}}{\frac {1}{x}} \\ \lim_{x \to \infty} \frac {cos\frac {1}{x}.\frac {-1}{x^2}}{\frac {-1}{x^2}} \\ \lim_{x \to \infty} cos\frac {1}{x} \\ cos\frac {1}{\infty} \\ cos0 = 1$