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

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

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,
$$\lim_{h\rightarrow0}\frac{100}{(10h-1)^{11}+2}=100$$

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