AMU MCA Continuity Previous Year Questions (PYQs)
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The function $f(x)=\dfrac{1 - \sin x + \cos x}{1 + \sin x + \cos x}$ is not defined at $x=\pi$. The value of $f(\pi)$, so that $f(x)$ is continuous at $x=\pi$, is
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Solution
The function $f(x)=\sqrt{|x|-x}$ is continuous for
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Solution
Inside root: $|x|-x \ge 0$ for all $x$
Function is defined and continuous for all real $x$
Which of the following function is continuous at origin?
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Solution
$z=(a^2+b^2)x+by$
The continuous function $f:\mathbb{R}\to\mathbb{R}$ defined by
$f(x)=\sqrt{x^2+1}$
is
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Solution
Range: $[1,\infty)$
Not onto $\mathbb{R}$
Not one-one (since $f(x)=f(-x)$)
Let
$f(x,y)=\begin{cases}
0,& xy\ne0\
1,& xy=0
\end{cases}$
Which is true?
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Solution
Limit at $(0,0)$ depends on path.
So not continuous.
Partials do not exist.
Let
$f(x,y)=\begin{cases}
0,& xy\ne0\
1,& xy=0
\end{cases}$
Which is true?
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3
4
Solution
Limit at $(0,0)$ depends on path.
So not continuous.
Partials do not exist.
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