Advertisements
Advertisements
Question
Let f(x)= |cosx|. Then, ______.
Options
f is everywhere differentiable
f is everywhere continuous but not differentiable at n = nπ, n ∈ Z
f is everywhere continuous but not differentiable at x = `(2"n" + 1) pi/2, "n" ∈ "Z"`
None of these
Solution
Let f(x)= |cosx|. Then, f is everywhere continuous but not differentiable at x = `(2"n" + 1) pi/2, "n" ∈ "Z"`.
APPEARS IN
RELATED QUESTIONS
Differentiate the function with respect to x.
sin (x2 + 5)
Differentiate the function with respect to x.
`(sin (ax + b))/cos (cx + d)`
Differentiate w.r.t. x the function:
sin3 x + cos6 x
Does there exist a function which is continuos everywhere but not differentiable at exactly two points? Justify your answer?
If sin y = xsin(a + y) prove that `(dy)/(dx) = sin^2(a + y)/sin a`
If y = tan(x + y), find `("d"y)/("d"x)`
Differentiate `tan^-1 (sqrt(1 - x^2)/x)` with respect to`cos^-1(2xsqrt(1 - x^2))`, where `x ∈ (1/sqrt(2), 1)`
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 |x| is differentiable everywhere.
Show that the function f(x) = |sin x + cos x| is continuous at x = π.
`sin sqrt(x) + cos^2 sqrt(x)`
sinmx . cosnx
(x + 1)2(x + 2)3(x + 3)4
`cos^-1 ((sinx + cosx)/sqrt(2)), (-pi)/4 < x < pi/4`
`tan^-1 (secx + tanx), - pi/2 < x < pi/2`
If y = `sqrt(sinx + y)`, then `"dy"/"dx"` is equal to ______.
A function is said to be continuous for x ∈ R, if ____________.
If sin y = x sin (a + y), then value of dy/dx is
If `ysqrt(1 - x^2) + xsqrt(1 - y^2)` = 1, then prove that `(dy)/(dx) = - sqrt((1 - y^2)/(1 - x^2))`
Let c, k ∈ R. If f(x) = (c + 1)x2 + (1 – c2)x + 2k and f(x + y) = f(x) + f(y) – xy, for all x, y ∈ R, then the value of |2(f(1) + f(2) + f(3) + ... + f(20))| is equal to ______.
If f(x) = `{{:((sin(p + 1)x + sinx)/x,",", x < 0),(q,",", x = 0),((sqrt(x + x^2) - sqrt(x))/(x^(3//2)),",", x > 0):}`
is continuous at x = 0, then the ordered pair (p, q) is equal to ______.
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 ______.
If f(x) = `{{:(ax + b; 0 < x ≤ 1),(2x^2 - x; 1 < x < 2):}` is a differentiable function in (0, 2), then find the values of a and b.
If f(x) = `{{:(x^2"," if x ≥ 1),(x"," if x < 1):}`, then show that f is not differentiable at x = 1.
The function f(x) = x | x |, x ∈ R is differentiable ______.
If f(x) = | cos x |, then `f((3π)/4)` is ______.
The set of all points where the function f(x) = x + |x| is differentiable, is ______.
