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  • Choose the correct answer out of 4 options given against each Question If f(x) = 1 – x + x^2 – x^3 … –x^99 + x^100, then f’(1) is equal to A. 150 B. –50 C. –150 D. 50

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

If f(x) = 1 - x + x\textsuperscript{2} - x\textsuperscript{3} \ldots -x\textsuperscript{99} + x\textsuperscript{100}, then f’(1) is equal to
A. 150
B. –50
C. –150
D. 50

Answers (1)

\\ f \left( x \right) =1-x+x^{2}-x^{3}+ \ldots -x^{99}+x^{100} \\ \\ f^{'} \left( x \right) =0-1+2x-3x^{2}+ \ldots -99x^{98}+100x^{99} \\ \\ f^{'} \left( 1 \right) =-1+2-3+4- \ldots -99+100 \\ \\ = \left( 2-1 \right) + \left( 4-3 \right) + \left( 6-5 \right) + \ldots \left( 100-99 \right) =1+1+ \ldots +1~~ \left( \text{50 times} \right) =50 \\ \\

Hence, the answer is option D

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infoexpert21

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