Show that` (16(32^x)-2^(3x-2)* 4^(x+1))/(15*2^(x-1)*16^x) - (5*5^(x-1))/(sqrt(5^(2x))` is given by

int(2x+5)/(sqrt(x^(2)+3x+1))

16. "4^(x)-3^(x-(1)/(2))=3^(x+(1)/(2))-2^(2x-1).

If f(x)=2^(3x-5) , find f^(-1)(16)

((x)/(3)-(2)/(5))/((3)/(4)-2x)=(16)/(15)

lim_(xrarr 1) (x^(2^(32))-2^32x+4^16-1)/((x-1)^2) is equal to

Which of the following expressions are polynomials ? In case of a polynomial , write its degree. (i) x^(5)-2x^(3)+x+sqrt(3) (ii) y^(3)+sqrt(3)y (iii) t^(2)-(2)/(5)t+sqrt(5) (iv) x^(100)-1 (v) (1)/(sqrt(2))x^(2)-sqrt(2)x+2 (vi) x^(-2)+2x^(-1)+3 (vii) 1 (viii) (-3)/(5) (ix) (x^(2))/(2)-(2)/(x^(2)) (x) root(3)(2)x^(2)-8 (xi) (1)/(2x^(2)) (xii) (1)/(sqrt(5))x^(1//2)+1 (xiii) (3)/(5)x^(2)-(7)/(3)x+9 (xiv) x^(4)-x^(3//2)+x-3 (xv) 2x^(3)+3x^(2)+sqrt(x)-1

The value of k for which f(x)={{:(,(x^(2^(32))-2^(32)x+4^(16)-1)/((x-1)^(2)),x ne 1),(,k,x=1):} is continuous at x=1, is

The value of k for which f(x)={{:(,(x^(2^(32))-2^(32)x+4^(16)-1)/((x-1)^(2)),x ne 1),(,k,x=1):} is continuous at x=1, is

Using properties of proportion, solve for x : (i) (sqrt(x + 5) + sqrt(x - 16))/ (sqrt(x + 5) - sqrt(x - 16)) = (7)/(3) (ii) (sqrt(x + 1) + sqrt(x - 1))/ (sqrt(x + 1) - sqrt(x - 1)) = (4x -1)/(2) . (iii) (3x + sqrt(9x^(2) -5))/(3x - sqrt(9x^(2) -5)) = 5 .

Evaluate: int{(2x-3)^(5)+(1)/((7x-5)^(3))+(1)/(sqrt(5x-4))+(1)/(2-3x)+sqrt(3x+2)}dx