# Calculus: Other Calculus Problems – #7724

Question: Find the following limits

(a) $$\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin x}{{{e}^{x}}-x-1}$$

(b) $$\underset{t\to 0}{\mathop{\lim }}\,\frac{t-\ln \left( 1+2t \right)}{{{t}^{2}}}$$

(c) $$\underset{n\to \infty }{\mathop{\lim }}\,{{\left( 1+\frac{1}{n} \right)}^{n}}$$

(d) $$\underset{x\to \infty }{\mathop{\lim }}\,{{x}^{\frac{1}{x}}}$$

(e) $$\underset{x\to 0}{\mathop{\lim }}\,\frac{{{\pi }^{x}}-{{3}^{x}}}{x}$$

(f) $$\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,{{x}^{1-\cos x}}$$

(g) $$\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,\left( \frac{1}{x}-\frac{1}{\ln \left( x+1 \right)} \right)$$