Advertisements
Advertisements
प्रश्न
Let f(x)= |cosx|. Then, ______.
विकल्प
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
उत्तर
Let f(x)= |cosx|. Then, f is everywhere continuous but not differentiable at x = `(2"n" + 1) pi/2, "n" ∈ "Z"`.
APPEARS IN
संबंधित प्रश्न
Differentiate the function with respect to x.
cos (sin x)
Differentiate the function with respect to x.
sin (ax + b)
Differentiate the function with respect to x.
`cos x^3. sin^2 (x^5)`
Differentiate w.r.t. x the function:
sin3 x + cos6 x
if y = `[(f(x), g(x), h(x)),(l, m,n),(a,b,c)]`, prove that `dy/dx` =`|(f'(x), g'(x), h'(x)),(l,m, n),(a,b,c)|`
Discuss the continuity and differentiability of the
If sin y = xsin(a + y) prove that `(dy)/(dx) = sin^2(a + y)/sin a`
If y = tanx + secx, prove that `("d"^2y)/("d"x^2) = cosx/(1 - sinx)^2`
cos |x| is differentiable everywhere.
sinn (ax2 + bx + c)
`cos(tan sqrt(x + 1))`
sinmx . cosnx
(x + 1)2(x + 2)3(x + 3)4
`cos^-1 ((sinx + cosx)/sqrt(2)), (-pi)/4 < x < pi/4`
`tan^-1 (sqrt((1 - cosx)/(1 + cosx))), - pi/4 < x < pi/4`
`sec^-1 (1/(4x^3 - 3x)), 0 < x < 1/sqrt(2)`
If xm . yn = (x + y)m+n, prove that `("d"^2"y")/("dx"^2)` = 0
A function is said to be continuous for x ∈ R, if ____________.
The rate of increase of bacteria in a certain culture is proportional to the number present. If it doubles in 5 hours then in 25 hours, its number would be
If sin y = x sin (a + y), then value of dy/dx is
Let f: R→R and f be a differentiable function such that f(x + 2y) = f(x) + 4f(y) + 2y(2x – 1) ∀ x, y ∈ R and f’(0) = 1, then f(3) + f’(3) is ______.
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) = `{{:(x^2"," if x ≥ 1),(x"," if x < 1):}`, then show that f is not differentiable at x = 1.
The set of all points where the function f(x) = x + |x| is differentiable, is ______.