taylor series

Taylor series expansion of $$f\left( x \right) = \int\limits_0^x {{e^{ - \left( {{{{t^2}} \over 2}} \right)}}} dt$$ around 𝑥 = 0 has the form f(x) = $${a_0} + {a_1}x + {a_2}{x^2}...

Let $$\,\,f\left( x \right) = {e^{x + {x^2}}}\,\,$$ for real $$x.$$ From among the following. Choose the Taylor series approximation of $$f$$ $$(x)$$ around $$x=0,$$ which includes...

The Taylor series expansion of $$3$$ $$sin$$ $$x$$ $$+2cos$$ $$x$$ is

The Taylor series expansion of $$\,\,{{\sin x} \over {x - \pi }}\,\,$$ at $$x = \pi $$ is given by

Which of the following function would have only odd powers of $$x$$ in its Taylor series expansion about the point $$x=0$$ ?

In the Taylor series expansion of $${e^x} + \sin x$$ about the point $$x = \pi ,$$ the coefficient of $${\left( {x = \pi } \right)^2}$$ is

For the function $${e^{ - x}},$$ the linear approximation around $$x=2$$ is

For $$\left| x \right| < < 1,\,\cot \,h\left( x \right)\,\,\,$$ can be approximated as

The third term in the taylor's series expansion of $${e^x}$$ about $$'a'$$ would be ________.