A) \[0\]
B) \[-100\]
C) \[100\]
D) \[200\]
Correct Answer: A
Solution :
[a] \[f(-x)=f(x)\] \[\Rightarrow \,\,\,\,\,f'(-x)=f'(x)\] \[f'(1)=-5\] \[\Rightarrow \,\,\,\,\,\,f'(-1)=5\] Also, \[f(2+x)=f(2-x)\] \[\Rightarrow \,\,\,\,\,\,\,\,\,f'(2+x)=-f'(2-x)\] \[\Rightarrow \,\,\,\,\,\,\,\,\,f'(3)=-f'(1)=5\] \[\therefore \,\,\,\,\sum\limits_{r=0}^{100}{{{(-1)}^{r}}\,f'(r)=f'(0)-f'(1)+f'(2)-f'(3)+}\] \[....-f'(99)+f'(100)=0\]You need to login to perform this action.
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