If `x in R` show that `(1)/(3x+1)+(1)/(x+1)-(1)/((3x+1)(x+1))` does not lies between 1 and 4.

int (x^3-1)/((x^4+1)(x+1)) dx is

lim_(x rarr1)(1)/((x-1))((1)/(x+3)-(2)/(3x+5))

Solve the equation (12x-1)(6x-1)(4x-1)(3x-1)=5

If (1)/(x)+(1)/(y)=(1)/(4) and (1)/(x)-(1)/(y)=(3)/(4) , then x=

The real number k for which the equation, 2x^3+""3x""+""k""=""0 has two distinct real roots in [0, 1] (1) lies between 2 and 3 (2) lies between -1 and 0 (3) does not exist (4) lies between 1 and 2

The real number k for which the equation, 2x^3+""3x""+""k""=""0 has two distinct real roots in [0, 1] (1) lies between 2 and 3 (2) lies between -1 and 0 (3) does not exist (4) lies between 1 and 2

lim_{x \to 1} (3x)/(x-1)

Solve the following equations : (1)/(x-1)-(1)/(x)=(1)/(x+3)-(1)/(x+4)

If (x^(2) + 1)/(x)= 3(1)/(3) and x gt 1 , find x^(3)- (1)/(x^(3))

((x+1))/((2x-1)(3x+1))=A/((2x-1))+B/((3x+1)) rArr 16A+9B=