मराठी

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

Advertisements
Advertisements

प्रश्न

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

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर
Advertisements

उत्तर

This statement is False.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Continuity And Differentiability - Solved Examples [पृष्ठ १०६]

APPEARS IN

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

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Differentiate the function with respect to x.

`sec(tan (sqrtx))`


Differentiate the function with respect to x.

`cos (sqrtx)`


Differentiate the function with respect to x:

(3x2 – 9x + 5)9


Differentiate the function with respect to x:

`sin^(–1)(xsqrtx), 0 ≤ x ≤ 1`


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 

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

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


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`


Differentiate `tan^-1 (sqrt(1 - x^2)/x)` with respect to`cos^-1(2xsqrt(1 - x^2))`, where `x ∈ (1/sqrt(2), 1)`


Let f(x)= |cosx|. Then, ______.


If u = `sin^-1 ((2x)/(1 + x^2))` and v = `tan^-1 ((2x)/(1 - x^2))`, then `"du"/"dv"` is ______.


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)`


`cos(tan sqrt(x + 1))`


sinx2 + sin2x + sin2(x2)


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`


`tan^-1 (secx + tanx), - pi/2 < x < pi/2`


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


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


If y = `sqrt(sinx + y)`, then `"dy"/"dx"` is equal to ______.


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


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.


The function f(x) = x | x |, x ∈ R is differentiable ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×