A) \[{{\sin }^{-1}}({{e}^{x}})+C\]
B) \[{{\cos }^{-1}}({{e}^{x}})+C\]
C) \[{{\sec }^{-1}}({{e}^{x}})+C\]
D) \[{{\tan }^{-1}}({{e}^{x}})+C\]
Correct Answer: C
Solution :
\[f(x)={{e}^{x}}g(x)\] On differentiating with respect to\[x,\]we get \[f(x)={{e}^{x}}g(x)+{{e}^{x}}g(x)\] At\[x=0\] \[f(0)={{e}^{0}}g(0)+{{e}^{0}}g(0)\] \[\Rightarrow \] \[f(0)=g(0)+g(0)\] \[=1+2\] \[\Rightarrow \] \[f(0)=3\]You need to login to perform this action.
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