Jump of a Discontinuity

Q. The function has jump discontinuity.

1. identity
2. cosine
3. greatest integer
4. logarithmic

Q. Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false:
(i) $1\in A$
(ii) $\left\{1,2,3\right\}\subset A$
(iii) $\left\{6,7,8\right\}\in A$
(iv) $\left\{\left\{4,5\right\}\right\}\subset A$
(v) $\varphi \in A$
(vi) $\varphi \subset A$

Q. Let R be the relation on Z defined by
R = {(a, b) : a, b ∈ Z, a − b is an integer}
Find the domain and range of R.

Q. What is the value of jump at x = 2, for f(x);
f(x) =

1. 2

Q. Let f(x) =$\left\{\begin{array}{cc}a& x>c\\ b& x\ge c\end{array}\right\}:a,b,cϵ-R$
if f(x) is discontinuous at x = c, and have a jump at x = c then the value of jump is -

Q.

1. 1

2. 1/2

3. log 2

4. zero

Q. What is the value of jump at x = 2, for f(x);
f(x) =

1. 2

Q.

Find the function in which the function having a jump discontinuity among the following.

1. $f\left(x\right)=\{\begin{array}{c}{x}^2+1\forall x\in R-\left\{10\right\}\\ 15x=10\end{array}$

2. $f\left(x\right)=\{\begin{array}{c}{x}^2+1\forall x\in (-\infty ,5)\\ x^2-1\forall x\in [5,\infty ]\end{array}$

3. $f\left(x\right)=\frac{x}{x-1}$

4. $f\left(x\right)=\frac{x}{x^2-1}$

Q.

Find the function in which the function having a jump discontinuity among the following.

1. $f\left(x\right)=\{\begin{array}{c}{x}^2+1\forall x\in (-\infty ,5)\\ x^2-1\forall x\in [5,\infty ]\end{array}$

2. $f\left(x\right)=\frac{x}{x-1}$

3. $f\left(x\right)=\frac{x}{x^2-1}$

4. $f\left(x\right)=\{\begin{array}{c}{x}^2+1\forall x\in R-\left\{10\right\}\\ 15x=10\end{array}$

Q. Let f(x) =$\left\{\begin{array}{cc}a& x>c\\ b& x\ge c\end{array}\right\}:a,b,cϵ-R$
if f(x) is discontinuous at x = c, and have a jump at x = c then the value of jump is -

1. undefined