NEET 2025 Reward Announcement !   *   Join the SATHEE channel for the latest updates- Click Here to Join the Channel.

CONTINUITY AND DIFFERENTIABILITY

M
Let $f: R \rightarrow R$ be a continuous function such that $f(3 x)-f(x)=x$. If $f(8)=7$, then $f(14)$ is equal to:
Replies
8
Views
111
Ashutosh
Ashutosh
S
Let $f: \mathrm{R} \rightarrow \mathrm{R}$ satisfy the equation $f(x+y)=f(x)f ( y )$ for all $x$, $y \in \mathbb{R}$ and $f(x) \neq 0$ for any
Replies
1
Views
56
LiveDoubtClearing
L
V
Question: Show that \( f(x) = |x| \) is not differentiable at \( x = 0 \).
Replies
0
Views
4
Vineet.ForumSolutions
V
V
If \( f(2) = 2 \) and \( f'(2) = 1 \), then find \( \lim_{x \to 2} \frac{xf(2) - 2f(x)}{x - 2} \)
Replies
0
Views
4
Vineet.ForumSolutions
V
V
Let f(x) = { 1, x ≤ -1 |x|, -1 < x < 1 x, x ≥ 1 } Then, f is (a) continuous at x = -1 (b) differentiable at x = -1 (c)
Replies
0
Views
4
Vineet.ForumSolutions
V
V
The set of points where the function f(x) given by f(x) = |x-3|cos x is differentiable, is (a) R (b) R-{3} (c) (0,∞) (d) none of these
Replies
0
Views
4
Vineet.ForumSolutions
V
V
If f(x) = { (1-cos x)/(x sin x), x ≠ 0 1/2, x = 0 then at x = 0, f(x) is (a) continuous and differentiable (b) differentia
Replies
0
Views
4
Vineet.ForumSolutions
V
V
Question: If f(x) = { 1 + e^(1/x), x ≠ 0 0, x = 0 } then f(x) is (a) continuous as well as differentiable at x = 0 (b) continuous but not diff
Replies
0
Views
4
Vineet.ForumSolutions
V
V
If f(x) = |3−x| + ⌈3+x⌉, where ⌈x⌉ denotes the least integer greater than or equal to x, then f(x) is (a) continuous and differentiable at x = 3 (b)
Replies
0
Views
4
Vineet.ForumSolutions
V
V
Let f(x) = a + b|x| + c|x|⁴, where a, b, and c are real constants. Then, f(x) is differentiable at x = 0, if (a) a = 0 (b) b = 0 (c) c = 0 (d) none of
Replies
0
Views
4
Vineet.ForumSolutions
V
V
The function f(x) = (sin(π[x−π])), where [ ] denotes the greatest integer function, is (a) continuous as well as differentiable for all x ∈ R (b) cont
Replies
0
Views
3
Vineet.ForumSolutions
V
V
The function f(x) = |cosx| is (a) differentiable at x = (2n+1)π/2, n∈Z (b) continuous but not differentiable at x = (2n+1)π/2, n∈Z (c) neither differ
Replies
0
Views
4
Vineet.ForumSolutions
V
V
The function f(x) = 1 + |cos x| is (a) continuous nowhere (b) continuous everywhere (c) not differentiable at x = 0 (d) not differentiable at x = nπ,
Replies
0
Views
4
Vineet.ForumSolutions
V
V
Let f(x) = |cos x|. Then, (a) f(x) is everywhere differentiable (b) f(x) is everywhere continuous but not differentiable at x = nπ, n ∈ Z (c) f(x) is
Replies
0
Views
6
Vineet.ForumSolutions
V
V
Let f(x) = |sin x|. Then, (a) f(x) is everywhere differentiable. (b) f(x) is everywhere continuous but not differentiable at x = nπ, n ∈ Z (c) f(x) is
Replies
0
Views
5
Vineet.ForumSolutions
V
V
Let f(x) = { ax² + 1, x > 1 x + 1/2, x ≤ 1 } Then, f(x) is derivable at x = 1, if (a) a = 2 (b) b = 1 (c) a = 0 (d) a = 1/2
Replies
0
Views
4
Vineet.ForumSolutions
V
V
The function f(x) = x − [x], where [ ] denotes the greatest integer function is (a) continuous everywhere (b) continuous at integer points only (c) co
Replies
0
Views
5
Vineet.ForumSolutions
V
V
Let f(x) = { 1|x| for |x| ≥ 1 ax² + b for |x| < 1 } If f(x) is continuous and differentiable at any point, then (A) a = 1/2, b = -3/2 (B) a =
Replies
0
Views
5
Vineet.ForumSolutions
V
V
If f(x) = ||loge||x||, then (a) f(x) is continuous and differentiable for all x in its domain (b) f(x) is continuous for all x in its domain but not d
Replies
0
Views
4
Vineet.ForumSolutions
V
V
If f(x) = |log(e^x)|, then (a) f'(1+) = 1 (b) f′(1−) = −1 (c) f'(1) = 1 (d) f'(1) = −1
Replies
0
Views
5
Vineet.ForumSolutions
V
You must log in or register to post here.
Back
Top