Question:
If \(f(x)=\begin{cases} xe^{-(\frac{1}{|x|}+\frac{1}{x})}; & \text{if } x\ne0 \text{ then} \\ 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ ; & \text{if }x=0\end{cases}\)
which of the following is correct ?
If \(f(x)=\begin{cases} xe^{-(\frac{1}{|x|}+\frac{1}{x})}; & \text{if } x\ne0 \text{ then} \\ 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ ; & \text{if }x=0\end{cases}\)
which of the following is correct ?
which of the following is correct ?
Updated On: Sep 15, 2024
- f(x) is continuous and f'(0) does not exist
- f(x) is not continuous
- f(x) is continuous and f'(0) also exists
- None of these
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The correct option is (A) : f(x) is continuous and f'(0) does not exist.
Was this answer helpful?
0
0
Top BCECE Mathematics Questions
- If $ {{I}_{m}}\left( \frac{z-1}{2z+1} \right)=-4, $ then locus of z is
- If $A = \begin{bmatrix}1&2&3\\ -1&1&2\\ 1&2&4\end{bmatrix} $ then $\left(A^{2} - 5A\right)A^{-1} = $
- If $e$ and $e^{'}$ are the eccentricities of hyperbolas $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ and its conjugate hyperbola, then the value of $\frac{1}{e^{2}}+\frac{1}{e^{'2}}$ is
- The equation of the circle concentric to the circle $ 2{{x}^{2}}+2{{y}^{2}}-3x+6y+2=0 $ and having area double the area of this circle, is
- The value of the $ \int_{{}}^{{}}{\frac{\sin x+\cos x}{3+\sin 2x}}dx $ is
View More Questions
Top BCECE Questions
- The term quaternary structure is used in the context of
- If $ {{I}_{m}}\left( \frac{z-1}{2z+1} \right)=-4, $ then locus of z is
- Which of the following is a soap?
- Which will reduce zinc oxide to zinc?
- Work done in turning a magnet of magnetic moment M by an angle of 90? from the mgnetic meridian is n times the corresponding work done to turn through an angle of 60?, where n is
View More Questions