A : The value of e lies between 2 and 3.
R : `e=1+(1)/(1!)+(1)/(2!)+(1)/(3!)+....`

(a) Find the value of e,correct to 3 decimal places e=1+(1)/(2!)+(1)/(3!)+(1)/(4!)...

In the network shown the potential difference between A and B is (R = r_(1) = r_(2) = r_(3) = 1 Omega, E_(1) = 3V, E_(2) = 2V, E_(3) = 1V )

P = 1 - (3)/(1!) + 9/(2!) - (27)/(3!) + ....... Q = 1+ (4)/(1!) +(16)/(2!) +(64)/(3!) + ........ R=log_(e)3+((log_e3)^2)/(2!)+((log_e3)^3)/(3!)+..... The ascending order of P,Q,R

if cos (1-i) = a+ib, where a , b in R and i = sqrt(-1) , then a. a = (1)/(2)(e-(1)/(e))cos 1, b = (1)/(2)(e+(1)/(e))sin 1 b. a=(1)/(2)(e+(1)/(e))cos 1,b=(1)/(2)(e-(1)/(e))sin 1 c. a=(1)/(2)(e+(1)/(e))cos 1,b=(1)/(2)(e+(1)/(e))sin 1 d. a=(1)/(2)(e-(1)/(e))cos 1,b=(1)/(2)(e-(1)/(e))sin 1

In the network shown the potential difference between A and B is R(=r_(1)=r_(2)=r_(3)=1Omega,E_(1)=3V,E_(2)=2V,E_(3)=1V)

Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-constant, and differentiable function such that f^(prime)(x)<2f(x)a n df(1/2)=1 . Then the value of int_(1/2)^1f(x)dx lies in the interval (a) (2e-1,2e) (b) (3-1,2e-1) (c) ((e-1)/2,e-1) (d) (0,(e-1)/2)

Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-constant, and differentiable function such that f^(prime)(x)<2f(x))a n df(1/2)=1 . Then the value of int_(1/2)^1f(x)dx lies in the interval (a) (2e-1,2e) (b) (3-1,2e-1) ((e-1)/2,e-1) (d) (0,(e-1)/2)

Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-constant, and differentiable function such that f^(prime)(x)<2f(x)a n df(1/2)=1 . Then the value of int_(1/2)^1f(x)dx lies in the interval (a) (2e-1,2e) (b) (3-1,2e-1) (c) ((e-1)/2,e-1) (d) (0,(e-1)/2)