If f(x) = `sqrt((( x + 1 ) ( x + 2 ) )/ (( x + 3 ) ( x + 6 )) )` then find f'(0)

(i) f(x) = sqrt(3 - 2x) (ii) f(x) = (1)/(sqrt(x + 2)) (iii) f(x) = 1 + x - [x - 2] . Find the domain of the following (23 - 24) :

If f (x)=((x+1)^(7)sqrt(1+x ^(2)))/((x^(2) -x+1)^(6)), then the value of f'(0) is equal to:

If f(x) = (sqrt(x+3)-2)/(x^(3)-1) , x != 1 , is continuous at x = 1, then f(1) is

Find 'c' of Lagrange's mean-value theorem for (i) f(x) = (x^(3) - 3x^(2) + 2x) " on " [0, (1)/(2)] (ii) f(x) = sqrt(25 -x^(2)) " on " [1, 5] (iii) f(x) = sqrt(x + 2)) " on " [4, 6]

f(x)=(2^x+2^(-x)(tanx)sqrt(tan^-1(2x^2-3x+1)))/(7x^2-3x-1)^3 , then find f'(0)

"Let "f(x)=((2^(x)+2^(-x))sin x sqrt(tan^(-1)(x^(2)-x+1)))/((7x^(2)+3x+1)^(3)) . Then find the value of f'(0).

"Let "f(x)=((2^(x)+2^(-x))sin x sqrt(tan^(-1)(x^(2)-x+1)))/((7x^(2)+3x+1)^(3)) . Then find the value of f'(0).

If 2f(x)-3f((1)/(x))=x^(2),x!=0, then find f(2)