If frac{1}{x(x^2 + 1)} = frac{A}{x} + frac{Bx | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the partial fraction decomposition: $\frac{1}{x(x^2 + 1)} = \frac{A}{x} + \frac{Bx + C}{x^2 + 1}$ Multiply both sides by $x(x^2 + 1)$: $1 =

Vedclass · Accepted Answer

$(1, -1, 0)$

Vedclass · Answer

(A) Given the partial fraction decomposition: $\frac{1}{x(x^2 + 1)} = \frac{A}{x} + \frac{Bx + C}{x^2 + 1}$ Multiply both sides by $x(x^2 + 1)$: $1 = A(x^2 + 1) + (Bx + C)x$ $1 = Ax^2 + A + Bx^2 + Cx$ $1 = (A + B)x^2 + Cx + A$ Comparing the coefficients of $x^2$,$x$,and the constant term on both sides: $A + B = 0$ $C = 0$ $A = 1$ Substituting $A = 1$ into $A + B = 0$,we get $1 + B = 0$,which implies $B = -1$. Thus,$(A, B, C) = (1, -1, 0)$.

If $\frac{1}{x(x^2 + 1)} = \frac{A}{x} + \frac{Bx + C}{x^2 + 1}$,then $(A, B, C) = $

Similar Questions

The temperature-entropy $(T-S)$ diagram of a reversible engine cycle is given in the figure. Its efficiency is

An $X$-ray tube is operated at $50 \ kV$. The minimum wavelength produced is ..... $\mathring{A}$.

Excess of which of the following in water causes blue baby syndrome disease?

Six moles of an ideal gas perform a cycle shown in the figure. If the temperatures are $T_A = 600 \ K, T_B = 800 \ K, T_C = 2200 \ K$,and $T_D = 1200 \ K$,the work done per cycle is ..... $kJ$.

In a sinusoidal wave,the time required for a particular point to move from maximum displacement to zero displacement is $0.170 \,s$. The frequency of the wave is ........ $Hz$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module