Question:medium

The function $f(x)=(2)^{\frac{1}{x}}$ is not continuous at}

Show Hint

Always look for denominators: if $x$ is in the denominator, $x=0$ is usually a point of discontinuity.

Updated On: Jul 3, 2026

$x=0$
$x=1$
$x=-1$
$x=2$

Show Solution

The Correct Option is A

Solution and Explanation

Was this answer helpful?

0

Top Questions on Real Analysis

Find the radius of convergence of the series \[ \sum_{n=0}^{\infty} \frac{(n!)^2}{(2n)!}\, x^n. \]
- IIT JAM MA - 2026
- Mathematics
- Real Analysis
View Solution
Determine whether the sequence \[ a_n = 1 - (-1)^n + \frac{1}{n} \] is convergent or divergent.
- IIT JAM MA - 2026
- Mathematics
- Real Analysis
View Solution
Let $G = P(N)$, where the operation is
\[ A \Delta B = A \cup B - A \cap B \] Which of the following is true?
- IIT JAM MA - 2026
- Mathematics
- Real Analysis
View Solution
Find the number of automorphisms of the cyclic group $\mathbb{Z}_n$ for $n = 30$.
- IIT JAM MA - 2026
- Mathematics
- Real Analysis
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in AP ECET BSc Mathematics exam

The integrating factor of $x \cos x \frac{dy}{dx} + (x \sin x + \cos x) y = 1$ is}

AP ECET BSc Mathematics - 2026
Differential equations

If $y = y(x)$ is the solution of $\left(\frac{2 + \sin x}{y + 1}\right) \frac{dy}{dx} + \cos x = 0$ with $y(0) = 1$, then $y\left(\frac{\pi}{2}\right) = $

AP ECET BSc Mathematics - 2026
Differential equations

The solution of $y^{4}dx + 2xy^{3}dy = \frac{ydx - xdy}{x^{3}y^{3}}$ is}

AP ECET BSc Mathematics - 2026
Differential equations

Which of the following is an integrating factor of $(x^{2} + y^{2} + 2x)dx + 2ydy = 0$?

AP ECET BSc Mathematics - 2026
Differential equations