maclaurin-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

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