English

The value of c in Rolle’s Theorem for the function f(x) = e x sinx, x ∈ π [0, π] is ______. - Mathematics

Advertisements
Advertisements

Question

The value of c in Rolle’s Theorem for the function f(x) = e x sinx, x ∈ π [0, π] is ______.

Options

  • `pi/6`

  • `pi/4`

  • `pi/2`

  • `(3pi)/4`

MCQ
Fill in the Blanks

Solution

The value of c in Rolle’s Theorem for the function f(x) = e x sinx, x ∈ π [0, π] is `(3pi)/4`.

shaalaa.com
  Is there an error in this question or solution?
Chapter 5: Continuity And Differentiability - Solved Examples [Page 105]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12
Chapter 5 Continuity And Differentiability
Solved Examples | Q 34 | Page 105

RELATED QUESTIONS

Verify Rolle’s theorem for the function f (x) = x2 + 2x – 8, x ∈ [– 4, 2].


Examine if Rolle’s Theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s Theorem from these examples?

f (x) = [x] for x ∈ [– 2, 2]


Verify Mean Value Theorem, if f (x) = x2 – 4x – 3 in the interval [a, b], where a = 1 and b = 4.


Verify Rolle’s theorem for the following function:

f (x) = x2 - 4x + 10 on [0, 4]


Verify Lagrange's Mean Value Theorem for the following function:

`f(x ) = 2 sin x +  sin 2x " on " [0, pi]`


f(x) = (x-1)(x-2)(x-3) , x ε[0,4], find if 'c' LMVT can be applied


Verify the Lagrange’s mean value theorem for the function: 
`f(x)=x + 1/x ` in the interval [1, 3]


Verify Langrange’s mean value theorem for the function:

f(x) = x (1 – log x) and find the value of  c in the interval [1, 2].


Verify Mean value theorem for the function f(x) = 2sin x + sin 2x on [0, π].


Verify mean value theorem for the function f(x) = (x – 3)(x – 6)(x – 9) in [3, 5].


f(x) = x(x – 1)2 in [0, 1]


f(x) = `sin^4x + cos^4x` in `[0, pi/2]`


f(x) = `sqrt(4 - x^2)` in [– 2, 2]


Discuss the applicability of Rolle’s theorem on the function given by f(x) = `{{:(x^2 + 1",",  "if"  0 ≤ x ≤ 1),(3 - x",",  "if"  1 ≤ x ≤ 2):}`


Find the points on the curve y = (cosx – 1) in [0, 2π], where the tangent is parallel to x-axis


f(x) = sinx – sin2x in [0, π]


Find a point on the curve y = (x – 3)2, where the tangent is parallel to the chord joining the points (3, 0) and (4, 1)


The value of c in Rolle’s theorem for the function f(x) = x3 – 3x in the interval `[0, sqrt(3)]` is ______.


If x2 + y2 = 1, then ____________.


The value of c in mean value theorem for the function f(x) = (x - 3)(x - 6)(x - 9) in [3, 5] is ____________.


If the greatest height attained by a projectile be equal to the horizontal range, then the angle of projection is


If A, G, H are arithmetic, geometric and harmonic means between a and b respectively, then A, G, H are


Value of' 'c' of the mean value theorem for the function `f(x) = x(x - 2)`, when a = 0, b = 3/2, is


If `1/(a + ω) + 1/(b + ω) + 1/(c + ω) + 1/(d + ω) = 1/ω`, where a, b, c, d ∈ R and ω is a cube root of unity then `sum 3/(a^2 - a + 1)` is equal to


Let a function f: R→R be defined as

f(x) = `{(sinx - e^x",", if x < 0),(a + [-x]",", if 0 < x < 1),(2x - b",", if x > 1):}`

where [x] is the greatest integer less than or equal to x. If f is continuous on R, then (a + b) is equal to ______.


P(x) be a polynomial satisfying P(x) – 2P'(x) = 3x3 – 27x2 + 38x + 1.

If function

f(x) = `{{:((P^n(x) + 18)/6, x ≠ π/2),(sin^-1(ab) + cos^-1(a + b - 3ab), x = π/2):}`

is continuous at x = ` π/2`, then (a + b) is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×