Question:medium

Consider the complex function \( f(z) = \cos z + e^{z^2} \). The coefficient of \( z^5 \) in the Taylor series expansion of \( f(z) \) about the origin is _____________ (rounded off to 1 decimal place).

Show Hint

The Taylor series expansion of a function about the origin involves terms with only integer powers of \( z \). Check each term carefully.

Updated On: Feb 3, 2026

Show Solution

Correct Answer: 0

Solution and Explanation

Was this answer helpful?

Questions Asked in GATE EE exam

Given an open-loop transfer function \(GH = \frac{100}{s}(s+100)\) for a unity feedback system with a unit step input \(r(t)=u(t)\), determine the rise time \(t_r\).

GATE EE - 2026
Control Systems

View Solution

In the series circuit shown containing a voltage source (V), a diode (D), a resistor (R), an inductor (L), and a capacitor (C), which of the following components are considered linear?

GATE EE - 2026
Control Systems

View Solution

Consider a linear time-invariant system represented by the state-space equation: \[ \dot{x} = \begin{bmatrix} a & b -a & 0 \end{bmatrix} x + \begin{bmatrix} 1 0 \end{bmatrix} u \] The closed-loop poles of the system are located at \(-2 \pm j3\). The value of the parameter \(b\) is:

GATE EE - 2026
Control Systems

View Solution

If P and Q are positive integers such that \(P^2 = Q^2 + 13\), find the value of the product \(PQ\).

GATE EE - 2026
Algebra

View Solution

Consider the complex function \( f(z) = \cos z + e^{z^2} \). The coefficient of \( z^5 \) in the Taylor series expansion of \( f(z) \) about the origin is _____________ (rounded off to 1 decimal place).

Show Hint

Correct Answer: 0

Solution and Explanation

Top Questions on Miscellaneous

Questions Asked in GATE EE exam