Let `f(x)={((alpha cotx)/x+beta/x^2,0<|x|lt=1),(1/3,x=0))` If `f(x)` is continuous at `x=0` then the value of `alpha^2+beta^2` is `1` b. `2` c. `5` d. 9

Let f(x)={{:((alphacotx)/(x)+(beta)/(x^(2))",",0ltxle1),((1)/(3)",",x=0):} If f(x) is continuous at x =0, then the value of alpha^(2)+beta^(2) is

Let alpha,beta be real number with 0<=alpha<=beta and f(x)=x^(2)-(alpha+beta)x+alpha beta such that int_(1)^(1)f(x)dx=1. Find the maximum value of int_(alpha)^( alpha)f(x)dx

If the function f(x)=x^(3)+alpha x^(2)+beta x+1 has maximum value at x=0 and minimum value at x=1, then (i)alpha=(2)/(3),beta=0 (ii) alpha=-(3)/(2),beta=0(iii)alpha=0,beta=(3)/(2)(iv) none of these

If f(x) = |(cos(x + alpha), cos(x+beta), cos(x + gamma)),(sin(x + alpha), sin(x+beta), sin(x + gamma)), (sin(beta - gamma), sin(gamma - alpha), sin(alpha - beta))| and f(2) = -2, then |sum_(r=1)^20 f(r)| equals

if f(x)=(sin (x+alpha)/(sin(x+beta))),alpha ne beta then f(x) has

If f(x) = |{:(cos (x+alpha),cos(x+beta),cos(x+gamma)),(sin (x+alpha),sin(x+beta),sin(x+gamma)),(sin(beta+gamma),sin(gamma+alpha),sin(alpha+beta)):}| then f(theta)-2f(phi)+f(psi) is equal to

Let f :R-> R be defined by f(x)={(alpha+sin[x]/x,if x>0 ),(2,if x=0),(beta+[(sinx-x)/x^3],if x<0):} where [x] denotes the integral part of x. If f continuous at x = 0 , then beta-alpha =

Let f(x) = ((x - gamma)(x - delta)) / ((x-alpha)(a-beta)) where, gamma < alpha < delta < beta , then which of the following is correct

Consider f (x) = x ^(ln x), and g (x) = e ^(2) x. Let alpha and beta be two values of x satisfying f (x) = g(x)( alpha lt beta) If h (x) = (f (x))/(g (x)) then h'(alpha) equals to: