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  • Choose the correct answer out of 4 options given against each Question If f(x)=1+x+x^2/2+x^3/3+⋯+x^100/100 then f’(1) is equal to A. 1/100 B. 100 C. does not exist D. 0

Choose the correct answer out of 4 options given against each Question

If f \left( x \right) =1+x+\frac{x^{2}}{2}+\frac{x^{3}}{3}+ \ldots +\frac{x^{100}}{100}  then f’(1) is equal to
A. 1/100
B. 100
C. does not exist
D. 0

Answers (1)

\\ f \left( x \right) =1+x+\frac{x^{2}}{2}+\frac{x^{3}}{3}+ \ldots +\frac{x^{100}}{100} \\ \\ f^{'} \left( x \right) =0+1+\frac{2x}{2}+\frac{3x^{2}}{3}+ \ldots +\frac{100x^{99}}{100} \\ \\ f^{'} \left( x \right) =0+1+x+x^{2}+ \ldots x^{99} \\ \\ f^{'} \left( 1 \right) =1+1+1+ \ldots +1~~ \left( \text{100 times} \right) =100 \\ \\

Hence, the answer is option B

 

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infoexpert21

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