engineering recuitment GATE ECE 2023-24 Test Series Engineering Mathematics Calculus Mean Value Theorem
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 all powers of x less than or equal to 3.
1
1 + x + x2 + x3
2
1 + x + \(\frac{3}{2}\) x2 + x3
3
1 + x + \(\frac{3}{2}\) x2 + \(\frac{7}{6}\) x3
4
1 + x + 3x2 + 7x3