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