Mathematics

# The function f(x) satisfying the equation ${f^2}\left( x \right) + 4f\left( x \right) \cdot f'\left( x \right) + {\left[ {f'\left( x \right)} \right]^2} = 0$ is

$f\left( x \right) = c.{e^{\left( {2 - \sqrt 3 } \right)x}}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Medium
Evaluate $\displaystyle\int_{0}^{2}(x^{2}-3x+2)\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard

$\displaystyle \int_{0}^{a}\frac{dx}{x+\sqrt{a^{2}-x^{2}}}=$
• A. $\pi$
• B. $\dfrac{\pi}{3}$
• C. $-\pi$
• D. $\dfrac{\pi}{4}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Prove that $\displaystyle\int^{\pi}_{-\pi}x^{12}\sin^9xdx=0$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
$\displaystyle \lim_{n\rightarrow \infty }\left ( \frac{1}{1-n^{2}}+\frac{2}{1-n^{2}}+ ...+\frac{n}{1-n^{2}} \right )$is equal to
• A. $0$
• B. $2$
• C. $\displaystyle 1+e^{-1}$
• D. None of the above

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\displaystyle \int _{ 0 }^{ 1 }{ \tan ^{ -1 }{ \left( \dfrac { 2x }{ 1-{ x }^{ 2 } } \right) dx } } =\dfrac{\pi}{a}-\ln a$. Find $a$.
• A. $1$
• B. $-1$
• C. None of these
• D. $2$