1.

If and `phi(x)=1/(1+e^(-x))` `S=phi(5) +phi(4) +phi(3) + ..+phi(-3) + phi (-4) + phi(-5)` then the value of S isA. 5B. `11//2`C. 6D. `13//2`

Answer» Correct Answer - 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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