मराठी

Cos |x| is differentiable everywhere. - Mathematics

Advertisements
Advertisements

प्रश्न

cos |x| is differentiable everywhere.

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर
Advertisements

उत्तर

This statement is True.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Continuity And Differentiability - Solved Examples [पृष्ठ १०७]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 5 Continuity And Differentiability
Solved Examples | Q 46 | पृष्ठ १०७

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Differentiate the function with respect to x.

sin (ax + b)


Differentiate the function with respect to x.

`sec(tan (sqrtx))`


Differentiate the function with respect to x. 

cos x3 . sin2 (x5)


Differentiate the function with respect to x. 

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


Differentiate the function with respect to x:

sin3 x + cos6 x


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.


Does there exist a function which is continuos everywhere but not differentiable at exactly two points? Justify your answer?


Discuss the continuity and differentiability of the 

\[f\left( x \right) = \left| x \right| + \left| x - 1 \right| \text{in the interval} \left( - 1, 2 \right)\]

If sin y = xsin(a + y) prove that `(dy)/(dx) = sin^2(a + y)/sin a`


`"If y" = (sec^-1 "x")^2 , "x" > 0  "show that"  "x"^2 ("x"^2 - 1) (d^2"y")/(d"x"^2) + (2"x"^3 - "x") (d"y")/(d"x") - 2 = 0`


Let f(x) = x|x|, for all x ∈ R. Discuss the derivability of f(x) at x = 0


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


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


`sin sqrt(x) + cos^2 sqrt(x)`


sinx2 + sin2x + sin2(x2)


`sin^-1  1/sqrt(x + 1)`


`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`


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


`tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2))), -1 < x < 1, x ≠ 0`


For the curve `sqrt(x) + sqrt(y)` = 1, `"dy"/"dx"` at `(1/4, 1/4)` is ______.


If k be an integer, then `lim_("x" -> "k") ("x" - ["x"])` ____________.


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 ____________.


If `y = (x + sqrt(1 + x^2))^n`, then `(1 + x^2) (d^2y)/(dx^2) + x (dy)/(dx)` is


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 `ysqrt(1 - x^2) + xsqrt(1 - y^2)` = 1, then prove that `(dy)/(dx) = - sqrt((1 - y^2)/(1 - x^2))`


A particle is moving on a line, where its position S in meters is a function of time t in seconds given by S = t3 + at2 + bt + c where a, b, c are constant. It is known that at t = 1 seconds, the position of the particle is given by S = 7 m. Velocity is 7 m/s and acceleration is 12 m/s2. The values of a, b, c are ______.


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 ______.


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 ______.


Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×