limits

Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined as follows: $$ f(x)=\left\{\begin{array}{cc} c_1 e^x-c_2 \log _e\left(\frac{1}{x}\right), & \text { if } x>0 \\...

The value of the following limit is _____________. $$\mathop {\lim }\limits_{x \to {0^ + }} {{\sqrt x } \over {1 - {e^{2\sqrt x }}}}$$

The value of $$\mathop {\lim }\limits_{x \to 1} {{{x^7} - 2{x^5} + 1} \over {{x^3} - 3{x^2} + 2}}.$$

$$\mathop {\lim }\limits_{x \to 4} {{\sin \left( {x - 4} \right)} \over {x - 4}} = \_\_\_\_\_\_\_.$$

$$\,\,\mathop {\lim }\limits_{x \to \infty } \,{x^{1/x}}\,\,$$ is

Which one of the following functions is continuous at $$x = 3$$?

Which one of the following functions is continuous at $$x=3?$$

What is the value of $$\mathop {\lim }\limits_{n \to \infty } {\left[ {1 - {1 \over n}} \right]^{2n}}?$$

$$\mathop {Lim}\limits_{x \to 0} \,{{Si{n^2}x} \over x} = \_\_\_\_.$$

$$\mathop {Lim}\limits_{x \to \infty } {{{x^3} - \cos x} \over {{x^2} + {{\left( {\sin x} \right)}^2}}} = \_\_\_\_\_\_.$$