If `varphi(x)=1/(1+e^(-x))` and `S=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`

Evaluate: int_(pi/4)^((3pi)/4) varphi/(1-sinvarphi)d varphi

If varphi(x) is differentiable function AAx in R and a in R^+ such that varphi(0)=varphi(2a),varphi(a)=varphi(3a)a n dvarphi(0)!=varphi(a) then show that there is at least one root of equation varphi^(prime)(x+a)=varphi^(prime)(x)in(0,2a)

If varphi(x) is a polynomial function and varphi^(prime)(x)>varphi(x)AAxgeq1a n dvarphi(1)=0, then varphi(x)geq0AAxgeq1 varphi(x)

If varphi(x) is a polynomial function and varphi^(prime)(x)>varphi(x)AAxgeq1a n dvarphi(1)=0, then varphi(x)geq0AAxgeq1 varphi(x)

If tantheta=1/2a n dt a nvarphi=1/3, then the value of theta+varphi is pi/6 (b) pi (c) 0 (d) pi/4

If (a+b)tan(theta-varphi)=(a-b)tan(theta+varphi),\ t h e n(sin(2theta))/("sin"(2varphi)) is equal to a. a b b. a/b c. b/a d. a^2b^2

If sintheta=5sin(theta+varphi),t h e ntan(theta+varphi)= (sinvarphi)/(cosvarphi-3) b. (sinvarphi)/(cosvarphi+3) c. (sinvarphi)/(cosvarphi-5) d. (cosvarphi)/(sinvarphi+5)

varphi ^2=0 represents

If the function f(x) increases in the interval (a , b),a n dvarphi(x) [f(x)]^2 , then varphi(x) increases in (a , b) varphi(x) decreases in (a , b) we cannot say that varphi(x) increases or decreases in (a , b)dot none of these

If for the function varphi(x) = lambdax^2+7x-4 , varphi' (5) = 97, find lambda .