taylor series

$\int \left(x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \dots\right) dx$ is equal to

$$\int {\left( {x - {{{x^2}} \over 2} + {{{x^3}} \over 3} - {{{x^4}} \over 4} + ....} \right)dx} $$ is equal to :

For a small value of h, the Taylor series expansion for f(x+h) is

The quadratic approximation of $$f\left( x \right) = {x^3} - 3{x^2} - 5\,\,$$ at the point $$x=0$$ is

The infinite series $$1 + x + {{{x^2}} \over {2!}} + {{{x^3}} \over {3!}} + {{{x^4}} \over {4!}} + ........$$ corresponds to

Limit of the following series as $$x$$ approaches $${\pi \over 2}$$ is $$f\left( x \right) = x - {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} - {{{x^7}} \over {7!}} + - - - - - $$

The Taylor series expansion of sin $$x$$ about $$x = {\pi \over 6}$$ is given by

A discontinuous real function can be expressed as

The Taylor's series expansion of sin $$x$$ is ______.