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If varphi(x)=1/(1+e^(-x))a n dS=varphi(5...

If `varphi(x)=1/(1+e^(-x))a n dS=varphi(5)+varphi(4)+varphi(3)++varphi(-3)+varphi(-4)+varphi(-5)` , then the value of `S` is. a. 5 b. 11/2 c. 6 d. 13/2

A

5

B

`11//2`

C

6

D

`13//2`

Text Solution

Verified by Experts

The correct Answer is:
B
Here `phi(-x)=(1)/(1+e^(x)).`
`"So, "phi(x)+phi(-x)=(1)/(1+e^(-x))+(1)/(1+e^(x))`
`=(e^(x))/(e^(x)+1)+(1)/(1+e^(x))=(e^(x)+1)/(e^(x)+1)=1`
`therefore" S"={phi(5)+phi(-5)}+...+{phi(1)+phi(-1)}+phi(0)`
`=1+1+1+1+1+phi(0)=5+(1)/(1+e^(0))=5+(1)/(2)=(11)/(2)`
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