`\lim _{x\to 0}(\frac{1}{e^x-1}-\frac{1}{x}\)`

frac{1}{sqrt7-4} frac{1}{sqrt11-7}

x frac{dy}{dx} = y - xcos^2 frac{y}{x}

lim_(x->e frac{logx-loge}{x-e}

int frac {dx}{x(x^4+1)

int frac{x}{x^2sqrt(x^4-1)} dx

If z(x+y)= x^2 +y^2 show that (frac{delz}{delx}-frac{del z}{del y})^2 = 4 (1- frac{delz}{delx}+frac{delz}{dely})

If the roots of the equation frac{alpha}{x-alpha}+frac{beta}{x-beta}=1 be equal in magnitude but opposite in sign , then alpha+beta is equal to

lim _{x \rightarrow 0} {e^x+sin x -1}/{log (1+x)}

lim_(x->1) (1-x^2) ^ frac{1}{log(1-x)}

lim_(xto0)((e^(x)-1)/x)^(1//x)