Non Removable Discontinuities

Q.

What is the limit of a function in calculus?

Q.

$f\left(x\right)=\left[x\right]$ is discontinuous at $x=1$ because

1. Value of function is not defined

2. Value of $f\left(x\right)$ is finite but not equal to the limit

3. Statement wrong, function is continuous

4. Limit doesn't exist

Q.

If a+b = $\alpha$, ab = $\beta$, and a, $H_1$, $H_2$, b form H.P, then $\frac{1}{H_1}$ + $\frac{1}{H_2}$ equals to

1. 

2. 

3. 

4. 

Q.

What are the limit properties?

Q.

If both $\underset{x\to a}{lim}f\left(x\right)$ and $\underset{x\to a}{lim}g\left(x\right)$ and exist finitely and $\underset{x\to a}{lim}g\left(x\right)=0$, then
$\underset{x\to a}{lim}\frac{f\left(x\right)}{g\left(x\right)}=\frac{\underset{x\to a}{lim}f\left(x\right)}{\underset{x\to a}{lim}g\left(x\right)}$

1. False

2. True

Q. Evaluate the Given limit: $\underset{x\to 3}{lim}(x+3)$

Q.

Let $f\left(x\right)=\{\begin{array}{cc}x\left[\frac{1}{x}\right]+x\left[x\right]& \text{if}x\ne 0\\ 0& \text{if}x=0\end{array}$ where $[\cdot ]$ denotes the greatest integer function, then which of the following is true?

1. f(x) has a removable discontinuity at x=1

2. f(x) has a non- removable discontinuity at x=2.

3. f(x) is discontinuous at all positive integers.

4. None of these

Q.

$Letf\left(x\right)=\left[x\right]cos\left(\frac{\pi }{[x+2]}\right)where,\left[\right]denotesthegreatestintegerfunction.Then,thedomainoffis$

1. 

2. 

3. 

4. 

Q. A function f(x) can be continuous at a point 'a' if .

1. $\underset{x\to a}{lim}f\left(x\right)=\infty$
2. left limit $\ne$right limit
3. $\underset{x\to a}{lim}f\left(x\right)=0$

Q.

Find the value of $\underset{h\to 0}{lim}[2-h]+\underset{h\to 0}{lim}[2+h]$

Q.

$f\left(x\right)=\left[x\right]$ is discontinuous at $x=1$ because

1. Value of function is not defined

2. Value of $f\left(x\right)$ is finite but not equal to the limit

3. Limit doesn't exist

4. Statement wrong, function is continuous

Q.

In which of the following cases is the function f(x) discontinuous at a?

1. 

2. 

3. 

4. 

Q.

Findf(x), where f(x) =

Q.

$li{m}_{x\to 0}\left(\frac{3x+|x|}{7x-5|x|}\right)$=___

1. $\frac{3}{7}$

2. $\frac{1}{6}$

3. 2

4. does not exist

Q.

The given graph is discontinuous at $x=a$ because the limit doesn't exist at $x=a$

1. False

2. True

Q. If CLASS is coded as EOEXX, how would you code SCHOOL ?

1. UFTTLR
2. UFLTTR
3. UTFYLR
4. ULFYRT

Q.

Let $f\left(x\right)=\{\begin{array}{cc}x\left[\frac{1}{x}\right]+x\left[x\right]& \text{if}x\ne 0\\ 0& \text{if}x=0\end{array}$ where $[\cdot ]$ denotes the greatest integer function, then which of the following is true?

1. f(x) has a removable discontinuity at x=1

2. f(x) has a non- removable discontinuity at x=2.

3. f(x) is discontinuous at all positive integers.

4. None of these

Q.

discuss the continuity of function f(x)= |x|+|x-1| in interval [-1, 2]

Q.

The given graph is discontinuous at $x=a$ because the limit doesn't exist at $x=a$

1. True

2. False