Question

Evaluate the Given limit: $\lim_{x\rightarrow 0}$ $(x+1)^5-\frac{1}{x}$

Answer 1

$\lim_{x\rightarrow 0}$ $(x+1)^5-\frac{1}{x}$
Put x+1 = y so that y→1 as x → 0.
Accordingly, $\lim_{x\rightarrow 0}$ $(x+1)^5-\frac{1}{x}$ = \lim_{y\rightarrow 1}$$\frac{y^{5-1}}{y-1}
= $\lim_{y\rightarrow 1}$ $\frac{y^{5-1}}{y-1}$
=5
∴\lim_{x\rightarrow 0}$$(x+1)^5-\frac{1}{x} = 5