A) 0
B) \[\frac{1}{x+\sqrt{{{x}^{2}}+1}}\]
C) \[\frac{1}{\sqrt{{{x}^{2}}+1}}\]
D) None of these
Correct Answer: B
Solution :
[b] \[\underset{h\to 0}{\mathop{\lim }}\,\frac{\int\limits_{x}^{x+h}{\frac{dx}{z+\sqrt{{{z}^{2}}+1}}}}{h},\frac{0}{0}\] Use L' Hospital Rule \[\underset{h\to 0}{\mathop{\lim }}\,\frac{\frac{1}{x+h\sqrt{{{(x+h)}^{2}}+1}}.(0+1)-0}{1}\] \[=\frac{1}{x+\sqrt{{{x}^{2}}+1}}\]You need to login to perform this action.
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