Question
Discuss the continuity and differntiability of f(x) = |log |x||.
✓
Answer
f(x) = |log |x||
Since, it is an absolute function. So, it is continuous function. The graph of the function is as below:-
From the graph, it is clear that f(x) is not differentiable at x = -1, 1 but continuous for all x.
Since, it is an absolute function. So, it is continuous function. The graph of the function is as below:-
From the graph, it is clear that f(x) is not differentiable at x = -1, 1 but continuous for all x.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Determine P(E|F): A die is thrown three times, E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses.
A company produces two types of goods A and B, that require gold and silver. Each unit of type A requires 3 g of silver and 1 g of gold while that of type B requires 1 g of silver and 2 g of gold. The company can procure a maximum of 9 g of silver and 8 g of gold. If each unit of type A brings a profit of ₹ 40 and that of type B ₹ 50, formulate LPP to maximize profit.
Find the inverse of the matrix $\begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}$.
→Determine whether or not the definition of $*$ given below gives a binary operation. In the event that $*$ is not a binary operation give justification of this.
On $Z^+,$ defined $*$ by $a * b = a - b.$
Here, $Z^+$ denotes the set of all non-negative integers.
→On $Z^+,$ defined $*$ by $a * b = a - b.$
Here, $Z^+$ denotes the set of all non-negative integers.
Form the differential equation from the following primitives where constants are arbitrart:$\text{xy}=\text{a}^2$
→If $\text{P(A)}=0.3,\text{P(B)}=0.6,\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)=0.5,$ find $\text{P}(\text{A}\cup\text{B}).$
→Write the ratio in which the line segment joining (a, b, c) and (-a, -b, -c) is divided by the xy-plane.
Evaluate the following integrals:
$\int\limits^\text{x}_{0}\text{e}^{-\text{x}}\text{ dx}$
→$\int\limits^\text{x}_{0}\text{e}^{-\text{x}}\text{ dx}$
If $C_{ij}$ is the cofactor of the element $a_{ij}$ of the matrix $\text{A}=\begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix},$ then write the value of $a_{32}C_{32}$.
→A fair die is rolled. Consider events E = $\{1,\ 3,\ 5\},\ \text{F}=\{2,\ 3\}\ \text{and}\ \text{G}=\{2,\ 3,\ 4,\ 5\}.\ \text{Find}:$
$\text{P}(\text{E}|\text{G})\ \text{and}\ \text{P}(\text{G}|\text{E})$
→$\text{P}(\text{E}|\text{G})\ \text{and}\ \text{P}(\text{G}|\text{E})$