Advertisements
Advertisements
प्रश्न
If f(x) = `{{:(x^2"," if x ≥ 1),(x"," if x < 1):}`, then show that f is not differentiable at x = 1.
Advertisements
उत्तर
∵ f(x) = `{{:(x^2"," if x ≥ 1),(x"," if x < 1):}`
then f'(x) = `{{:(2x"," if x ≥ 1),(1"," if x < 1):}`
LHD of f(x) = 1
RHD of f(x) = 2x = 2
Since LHD ≠ RHD
It is not differentiable at x = 1.
संबंधित प्रश्न
Differentiate the function with respect to x:
sin3 x + cos6 x
Differentiate the function with respect to x:
`(5x)^(3cos 2x)`
Differentiate the function with respect to x:
`sin^(–1)(xsqrtx), 0 ≤ x ≤ 1`
Differentiate the function with respect to x:
`x^(x^2 -3) + (x -3)^(x^2)`, for x > 3
If f(x) = |x|3, show that f"(x) exists for all real x and find it.
If sin y = xsin(a + y) prove that `(dy)/(dx) = sin^2(a + y)/sin a`
If f(x) = x + 1, find `d/dx (fof) (x)`
If u = `sin^-1 ((2x)/(1 + x^2))` and v = `tan^-1 ((2x)/(1 - x^2))`, then `"du"/"dv"` is ______.
| COLUMN-I | COLUMN-II |
| (A) If a function f(x) = `{((sin3x)/x, "if" x = 0),("k"/2",", "if" x = 0):}` is continuous at x = 0, then k is equal to |
(a) |x| |
| (B) Every continuous function is differentiable | (b) True |
| (C) An example of a function which is continuous everywhere but not differentiable at exactly one point |
(c) 6 |
| (D) The identity function i.e. f (x) = x ∀ ∈x R is a continuous function |
(d) False |
`cos(tan sqrt(x + 1))`
`cos^-1 ((sinx + cosx)/sqrt(2)), (-pi)/4 < x < pi/4`
The differential coefficient of `"tan"^-1 ((sqrt(1 + "x") - sqrt (1 - "x"))/(sqrt (1+ "x") + sqrt (1 - "x")))` is ____________.
If `"f"("x") = ("sin" ("e"^("x"-2) - 1))/("log" ("x" - 1)), "x" ne 2 and "f" ("x") = "k"` for x = 2, then value of k for which f is continuous is ____________.
A function is said to be continuous for x ∈ R, if ____________.
Let S = {t ∈ R : f(x) = |x – π| (e|x| – 1)sin |x| is not differentiable at t}. Then the set S is equal to ______.
Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2.
Which expression defines the derivative of a real function \[f\] at a point \[c\] in its domain?
If \[u\] and \[v\] are differentiable functions, which formula is correct?
What is \[\frac{d}{dx}(\sin x)\]?
What is \[\frac{d}{dx}(\cos x)\]?
A function is differentiable at \[x=c\] when which condition holds?
Which limit is the left-hand derivative at \[x=c\]?
If \[f\] is differentiable at \[c\], which limit equals \[f'(c)\]?
When does a derivative exist?
