Removable Discontinuities

Q.

You can remove a removable discontinuity by

1. By redefining the domain of function appropriately

2. By redefining the function value at the point of discontinuity

3. By excluding the points where function goes to infinity

4. All of these

Q.

In the plot of the function below. Which is the point at which the discontinuity is of removable type?

1. p

2. All the above

3. q

4. r

Q.

In the plot of the function below. Which is the point at which the discontinuity is of removable type?

1. p

2. q

3. r

4. All the above

Q. Solve:


$\left(1\right)\underset{\mathrm{x}\to \mathrm{x}}{\mathrm{Lim}}\frac{1-{\cos }^3\mathrm{x}+{\sin }^3\mathrm{x}+\mathcal{l}\mathrm{n}\left(1+\cos \mathrm{x}\right)}{{\mathrm{x}}^2-1+2{\cos }^2\mathrm{x}+{\tan }^4\mathrm{x}+{\sin }^3\mathrm{x}}\mathrm{is}\mathrm{equal}\mathrm{to}-$

Q.

In the plot of the function below. Which is the point at which the discontinuity is of removable type?

1. p

2. r

3. q

4. All the above

Q. A discontinuous function can be made continuous by redefining the domain to exclude the points of discontinuities.

1. False

2. True