Limits and Deri...

The value of $$\displaystyle \lim_{x\rightarrow 0}\dfrac {1-\cos^{3}x}{x\sin x\cos x}$$ is

Integrate:
 $$lim_{x\rightarrow 0}\dfrac{(1-\cos{2x})^{2}}{2x\tan{x}-x\tan{2x}}$$

The value of $$\lim_{x \rightarrow 0} \left(\dfrac{\tan x}{x}\right)^{1/x^{3}}$$ is-

$$ \underset { x\rightarrow 0 }{ lim } \cfrac { { \left( 25 \right)  }^{ x }-2\left( 15 \right)^ x+{ 9 }^{ x } }{ cos6x-cos2x }  $$ is equal to :

$$Lt_{x\to 0} \dfrac{sin x - x+\dfrac{x^3}{6}}{x^5}=$$_________

If x + y = sin (x + y) then $$\dfrac{dy}{dx}$$ =

$${d}{dx}(sin^{5} x. sin5x) =$$

The value of $$\lim _{ x\rightarrow 0 }{ \dfrac { 1-\cos { ^{ 3 }x }  }{ x\sin { x\cos { x }  }  }  }$$ is

If the anti derivative of f(x) is $$e^x$$ and that of g(x) of cos x respectively, then $$\int f(x) cos x dx + \int g(x) e^x dx=$$_____________.

The ant derivative of $$\dfrac{1}{\left(21+x\tan x\right)^{2}}$$ with respect to $$x$$ is equal to