lim _(x arrow 0)(1+x)^(2)/(sin x)=

To find the limit \( \lim_{x \rightarrow 0}(1+x)^{\frac{2}{\sin x}} \), we can use the fact that \( (1+x)^{\frac{1}{x}} \) approaches as approaches 0.First, let's rewrite the expression in a form that makes it easier to apply this fact: Now, let \( y = (1+x)^{\frac{1}{\sin x}} \). We want to find the limit of as approaches 0.Since \( (1+x)^{\frac{1}{x}} \) approaches as approaches 0, we can write: Therefore, So, the limit is: