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

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

The value of the integral of the function $$\,\,g\left( {x,y} \right) = 4{x^3} + 10{y^4}\,\,$$ along the straight line segment from the point $$(0,0)$$ to the point $$(1,2)$$ in the $$xy$$ -plane is

For real values of $$x,$$ the minimum value of function $$f\left( x \right) = {e^x} + {e^{ - x}}\,\,$$ is