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
Construct a 2 × 3 matrix A = [aij] whose elements aij are give by:
aij = 2i - j
Write the position vector of a point dividing the line segment joining points A and B with position vectors $\vec{\text{a}}\text{ and }\vec{\text{b}}$ externally in the ratio 1 : 4, where $\vec{\text{a}}=2\hat{\text{i}}+3\hat{\text{j}}+4\hat{\text{k}}$ and $\vec{\text{b}}=-\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$.
→Six coins are tossed simultaneously. Find the probability of getting.
at least one head.
at least one head.
Let E and F be events with P (E) = $\frac{3}{5}$, P (F) = $\frac{3}{{10}}$ and $P(E \cap F)$ = $\frac{1}{5}$. Are E and F independent?
→Evaluate the following integrals:
$\int\frac{\cos\sqrt{\text{x}}}{\sqrt{\text{x}}}\text{ dx}$
→$\int\frac{\cos\sqrt{\text{x}}}{\sqrt{\text{x}}}\text{ dx}$
Evaluate the following integral:
$\int\frac{1}{\sqrt{\text{a}^2-\text{b}^2\text{x}^2}}\text{ dx}$
→$\int\frac{1}{\sqrt{\text{a}^2-\text{b}^2\text{x}^2}}\text{ dx}$
Differentiate the $\sqrt{e^{\sqrt{x}}}, x>0$ w.r.t. x.
→Find the components along the coordinate axis of the position vector of the following point:
S(4,-3)
Write the value of $\big[\hat{\text{i}}+\hat{\text{j}}\hat{\text{j}}+\hat{\text{k}}\hat{\text{k}}+\hat{\text{i}}\big].$
→Find the general solution of differential equation $\frac{d x}{d y}+(\tan y) x=\sec ^2 y$.
→