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|sinx| is a differentiable function for every value of x. - Mathematics

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प्रश्न

|sinx| is a differentiable function for every value of x.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
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उत्तर

This statement is False.

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अध्याय 5: Continuity And Differentiability - Solved Examples [पृष्ठ १०६]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 5 Continuity And Differentiability
Solved Examples | Q 45 | पृष्ठ १०६

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Differentiate the function with respect to x.

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`2sqrt(cot(x^2))`


Differentiate the function with respect to x:

sin3 x + cos6 x


Differentiate the function with respect to x:

`sin^(–1)(xsqrtx), 0 ≤ x ≤ 1`


Differentiate the function with respect to x:

`(cos^(-1)  x/2)/sqrt(2x+7)`, −2 < x < 2


Find `dy/dx`, if y = 12 (1 – cos t), x = 10 (t – sin t), `-pi/2 < t < pi/2`.


If f(x) = |x|3, show that f"(x) exists for all real x and find it.


If f(x) = x + 1, find `d/dx (fof) (x)`


If y = tan(x + y), find `("d"y)/("d"x)`


If y = tanx + secx, prove that `("d"^2y)/("d"x^2) = cosx/(1 - sinx)^2`


Differential coefficient of sec (tan–1x) w.r.t. x is ______.


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))`


sinx2 + sin2x + sin2(x2)


(sin x)cosx 


(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`


`tan^-1 (("a"cosx - "b"sinx)/("b"cosx - "a"sinx)), - pi/2 < x < pi/2` and `"a"/"b" tan x > -1`


`sec^-1 (1/(4x^3 - 3x)), 0 < x < 1/sqrt(2)`


`tan^-1 ((3"a"^2x - x^3)/("a"^3 - 3"a"x^2)), (-1)/sqrt(3) < x/"a" < 1/sqrt(3)`


If xm . yn = (x + y)m+n, prove that `("d"^2"y")/("dx"^2)` = 0


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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 ____________.


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


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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 ______.


If f(x) = | cos x |, then `f((3π)/4)` is ______.


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