Some important series `(i)(1+x)^(-1)` (ii)`(1-x)^(-1) ` (iii) `(1+x)^(-2)` (iv)`(1-x)^(-2)`

(i) 6x^(-2) (ii) (1)/(5)x^(5) (iii) (1)/(3x)

Expand using binomial theorem: (i) (1-2x)^(4) " " (ii) (x+2y)^(5) (iii) (x-(1)/(x))^(6) " "(iv) ((2x)/(3)=(3)/(2x))^(5) (v) (x^(2) +(2)/(x))^(6)" "(vi) (1+(1)/(x^(2)))^(4)

Write down the domain of : (i) f(x) = sin^(-1) x (ii) f(x) = cos^(-1)x (iii) f(x) = tan^(-1)x (iv) f(x) = sec^(-1) x

Find the derivative (i) x^(1//3) (ii) (2)/(x^(3//2)) (iii) 3x^(-1//4)

Find the derivative of the following functions from first principle. (i) x^3-27 (ii) (x" "" "1)" "(x" "" "2) (iii) 1/(x^2) (iv) (x+1)/(x-1)

Obtain the different coefficient of the following : (i) (x-1)(2x+5) (ii) (1)/(2x+1) (iii) (3x+4)/(4x+5) (iv) (x^(2))/(x^(3)+1)

If graph of y=(x-1)(x-2) is then draw the graph of the following (i) y=|(x-1)(x-2)| (ii) |y|=(x-1)(x-2) (iii) y=(|x|-1)(|x|-2) (iv) |(|x|-1)(|x|-2)| (v) |y|=|(|x|-1)(|x|-2)|

Find the domain of functions : (i) f(x)= 1/sqrt(1-cosx) (ii) (x^3-x+3)/(x^2-1) (iii) (3x)/(2x-8) (iv) x|x|

Which of the following function is even function? ( i )(a^(x)+1)/(a^(x)-1) (ii) x*(a^(x)+1)/(a^(x)-1) (iii) (a^(x)+a^(-x))/(a^(x)-a^(-x))( iv) none of these