Evaluate the following limit. lim_{hrightarrow0}frac{100}{(10h-1)^{11}+2}

Evaluate the following limit. lim_{hrightarrow0}frac{100}{(10h-1)^{11}+2}

Question
Limits and continuity
asked 2021-03-04
Evaluate the following limit.
\(\lim_{h\rightarrow0}\frac{100}{(10h-1)^{11}+2}\)

Answers (1)

2021-03-05
Given,
\(\lim_{h\rightarrow0}\frac{100}{(10h-1)^{11}+2}\)
Consider,
\(\lim_{h\rightarrow0}\frac{100}{(10h-1)^{11}+2}\)
Now substitute the limit h tends to 0 we get,
\(\lim_{h\rightarrow0}\frac{100}{(10h-1)^{11}+2}=\lim_{h\rightarrow0}\frac{100}{(10(0)-1)^{11}+2}\)
\(=\lim_{h\rightarrow0}\frac{100}{(0-1)^{11}+2}\)
\(=\lim_{h\rightarrow0}\frac{100}{-1+2}\)
\(=\frac{100}{1}\)
\(=100\)
Therefore,
\(\lim_{h\rightarrow0}\frac{100}{(10h-1)^{11}+2}=100\)
0

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