Mathematics

# If $\dfrac{3x^{2}+10x+13}{(x-1)^{4}}=\dfrac{A}{(x-1)^{2}}+\dfrac{B}{(x-1)^{3}}+\dfrac{C}{(x-1)^{4}}$ then descending order of $A,B,C$

$C, B, A$

##### SOLUTION
$\dfrac{3x^{2}+10x+13}{(x-1)^{4}}=\dfrac{A}{(x-1)^{2}}+\dfrac{B}{(x-1)^{3}}+\dfrac{C}{(x-1)^{4}}$
substitute $x-1=t\Rightarrow x=(t+1)$
$\dfrac{3(t+1)^{2}+10(t+1)+13}{t^{4}}=\dfrac{3t^{2}+16t+26}{t^{4}}$
$=\dfrac{3}{t^{2}}+\dfrac{16}{t^{3}}+\dfrac{26}{t^{4}}$
$=\dfrac{3}{(x-1)^{2}}+\dfrac{16}{(x-1)^{3}}+\dfrac{26}{(x-1)^{4}}$
So, decreasing order is
$C,B,A$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114

#### Realted Questions

Q1 Subjective Medium
Evaluate the following:
$\displaystyle \int_{-\pi/4}^{\pi/4} log(sin x + cos x)dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Multiple Correct Hard
Let $f\left ( x \right )$ be a non-constant twice differentiable function defined on $\left ( -\infty , \infty \right )$ such that $f\left ( x \right )= f\left ( 1-x \right )$ and $f{}'\displaystyle \left ( \frac{1}{4} \right )= 0$. Then which of the following is/are true?
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• C. $\displaystyle \int_{-\frac12}^{\frac12}f\left ( x+\dfrac12 \right )\sin x\: dx= 0$
• D. $\displaystyle \int_{0}^{\frac12}f\left ( t \right )e^{\sin \pi }dt= \displaystyle \int_{\frac12}^{1}f\left ( 1-t \right )e^{sin\pi }dt$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\int { { e }^{ x } } { \left( \dfrac { x-1 }{ { x }^{ 2 }+1 } \right) }^{ 2 }dx$
• A. $\dfrac { { xe }^{ x } }{ { x }^{ 2 }+1 } +c$
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1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Interagte : $\int {\dfrac{{\sec \theta }}{{\sec \theta + \tan \theta }}}$

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$