Limits Continuity And Differentiability

$$\begin{aligned} f(x) & =(1+2 x)^{1 / x}, & & x \neq 0 \\ & =e^2, & & x=0 \end{aligned}$$

$$\begin{aligned} f(x) & =\sin x-\cos x, & & x \neq 0 \\ & =-1, & & x=0 \end{aligned}$$

$$\begin{array}{rlr} f(x) & =\frac{e^{1 / x}-1}{e^{1 / x}+1}, & x \neq 0 \\ & =-1, & x=0 \end{array}$$

$$\begin{array}{rlr} f(x) & =\frac{e^{5 x}-e^{2 x}}{\sin 3 x}, & x \neq 0 \\ & =1, & x=0 \end{array}$$