Question

Coefficient of x in f(x)= $\left| \begin{matrix} x & (1 + \sin x)^{3} & \cos x \\ 1 & \log(1 + x) & 2 \\ x^{2} & (1 + x)^{2} & 0 \end{matrix} \right|$ is –

• A. 0
• B. 1
• C. – 2
• D. Cannot be determined

Answer 1

Answer: (C)

– 2

Answer 2

Coefficient of x in

$\left| \begin{matrix} x & \left( 1 + x - \frac{x^{3}}{3!} \right)^{3} & 1 - \frac{x^{2}}{2!}.... \\ 1 & x - \frac{x^{2}}{2} + ... & 2 \\ x^{2} & 1 + x^{2} & 0 \end{matrix} \right|$ Coefficient of x in

x & 1 & 1 \\ 1 & x & 2 \\ x^{2} & 1 & 0 \end{matrix} \right|$$ Coefficient of x in [x (0 – 2) – 1 (0 – 2x²) + 1 (1 – x²)] = – 2