मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Select the correct answer from the given alternatives: If f(x) = [x] for x ∈ (–1, 2) then f is discontinuous at - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Select the correct answer from the given alternatives:

If f(x) = [x] for x ∈ (–1, 2) then f is discontinuous at

पर्याय

  • x = –1, 0, 1, 2,

  • x = –1, 0, 1

  • x = 0, 1

  • x = 2

MCQ
Advertisements

उत्तर

If f(x) = [x] for x ∈ (–1, 2) then f is discontinuous at x = 0, 1

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Continuity - MISCELLANEOUS EXERCISE-8 [पृष्ठ १७७]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
पाठ 8 Continuity
MISCELLANEOUS EXERCISE-8 | Q (I) (10) | पृष्ठ १७७

संबंधित प्रश्‍न

Examine whether the function is continuous at the points indicated against them:
f(x) = `(x^2 + 18x - 19)/(x - 1)`        for x ≠ 1

      = 20                               for x = 1, at x = 1


Examine the continuity of `"f"(x)  {:(= sin x",",  "for"  x ≤ pi/4), (= cos x",",  "for"  x > pi/4):}}  "at"  x = pi/4`


Examine whether the function is continuous at the points indicated against them :

f(x) `{:(= x/(tan3x) + 2",",   "for"  x < 0),(= 7/3",",  "for"  x ≥ 0):}}  "at"  x = 0`


Find all the point of discontinuities of f(x) = [x] on the interval (− 3, 2).


Test the continuity of the following function at the point or interval indicated against them :

f(x)  `{:(= (sqrt(x - 1) - (x - 1)^(1/3))/(x - 2)",",  "for"  x ≠ 2),(= 1/5",",  "for"  x = 2):}}`at x = 2


Test the continuity of the following function at the point or interval indicated against them :

f(x) `{:(= ((27 - 2x)^(1/3) - 3)/(9 - 3(243 + 5x)^(1/5))",",  "for"  x ≠ 0),(= 2",",  "for"  x = 0):}}` at x = 0.


Identify discontinuities for the following function as either a jump or a removable discontinuity :

f(x) `{:(= x^2 - 3x - 2",",  "for"  x < -3),(= 3 + 8x",",  "for"  x > -3):}`


Show that following function have continuous extension to the point where f(x) is not defined. Also find the extension :

f(x) = `(1 - cos2x)/sinx`, for x ≠ 0


Show that following function have continuous extension to the point where f(x) is not defined. Also find the extension :

f(x) = `(3sin^2 x + 2cos x(1 - cos 2x))/(2(1 - cos^2x)`, for x ≠ 0


Discuss the continuity of the following function at the point indicated against them :

f(x)  `{:(=("e"^(1/x) - 1)/("e"^(1/x) + 1)",",  "for"  x ≠ 0),(= 1",", "for"  x = 0):}}` at x = 0


The following function has a removable discontinuity? If it has a removable discontinuity, redefine the function so that it becomes continuous :

f(x) `{:(=("e"^(5sinx) - "e"^(2x))/(5tanx - 3x)",",   "for"  x ≠ 0),(= 3/4",",   "for"  x = 0):}}` at x = 0


The following function has a removable discontinuity? If it has a removable discontinuity, redefine the function so that it become continuous :

f(x) `{:(= log_((1 + 3x)) (1 + 5x)",", "for"  x > 0),(=(32^x - 1)/(8^x - 1)",",  "for"  x < 0):}}` at x = 0


The following function has a removable discontinuity? If it has a removable discontinuity, redefine the function so that it become continuous :

f(x) = `((3 - 8x)/(3 - 2x))^(1/x)`, for x ≠ 0


The following function has a removable discontinuity? If it has a removable discontinuity, redefine the function so that it become continuous :

f(x) `{:(= 3x + 2",",  "for"  -4 ≤ x ≤-2),(= 2x - 3";",  "for"  -2 < x ≤ 6):}`


The following function has a removable discontinuity? If it has a removable discontinuity, redefine the function so that it become continuous :

f(x) `{:(= (x^3 - 8)/(x^2 - 4)",",  "for"  x > 2),(= 3",",  "for"  x = 2),(= ("e"^(3(x - 2)^2 - 1))/(2(x - 2)^2) ",",  "for"  x < 2):}`


If f(x) = `(sqrt(2 + sin x) - sqrt(3))/(cos^2x), "for"  x ≠ pi/2`, is continuous at x = `pi/2` then find `"f"(pi/2)`


If f(x) = `(cos^2 x - sin^2 x - 1)/(sqrt(3x^2 + 1) - 1)` for x ≠ 0, is continuous at x = 0 then find f(0)


If f(x) = `(4^(x - π) + 4^(π - x) - 2)/(x - π)^2` for x ≠ π, is continuous at x = π, then find f(π).


If f(x) `{:(= (24^x - 8^x - 3^x + 1)/(12^x - 4^x - 3^x + 1)",",  "for"  x ≠ 0), (= "k"",",  "for"  x = 0):}}` is continuous at x = 0, find k


Discuss the continuity of f(x) at x = `pi/4` where, 

f(x) `{:(= ((sinx + cosx)^3 - 2sqrt(2))/(sin 2x - 1)",", "for"  x ≠ pi/4),(= 3/sqrt(2)",", "for"  x = pi/4):}`


Select the correct answer from the given alternatives:

f(x) = `{:(= (2^(cotx) - 1)/(pi - 2x)",", "for"  x ≠ pi/2),(= log sqrt(2)",", "for"  x = pi/2):}`


Select the correct answer from the given alternatives:

If f(x) = `(1 - sqrt(2) sinx)/(pi - 4x), "for"  x ≠ pi/4` is continuous at x = `pi/4`, then `"f"(pi/4)` =


Select the correct answer from the given alternatives:

f(x) `{:(= ((16^x - 1)(9^x - 1))/((27^x - 1)(32^x - 1))",", "for"  x ≠ 0),(= "k"",", "for"  x = 0):}` is continuous at x = 0, then ‘k’ =


Discuss the continuity of the following function at the point(s) or on the interval indicated against them:

f(x) `{:(= (|x + 1|)/(2x^2 + x - 1)",", "for"  x ≠ -1),(= 0",", "for"  x = -1):}}` at x = – 1


Find a and b if following function is continuous at the point or on the interval indicated against them:

f(x) `{:(= (4tanx + 5sinx)/("a"^x - 1)",", "for"  x < 0),(= (9)/(log2)",", "for"  x = 0),(= (11x + 7x*cosx)/("b"^x - 1)",", "for"  x > 0):}`


Find f(a), if f is continuous at x = a where,

f(x) = `(1 + cos(pi x))/(pi(1 - x)^2)`, for x ≠ 1 and at a = 1


Solve using intermediate value theorem:

Show that 5x − 6x = 0 has a root in [1, 2]


If function `f(x)={((x^2-9)/(x-3), ",when "xne3),(k, ",when "x =3):}` is continuous at x = 3, then the value of k will be ______.


If f(x) = `{{:(tanx/x + secx",",   x ≠ 0),(2",",  x = 0):}`, then ______.


Let f be the function defined by

f(x) = `{{:((x^2 - 1)/(x^2 - 2|x - 1| - 1)",", x ≠ 1),(1/2",", x = 1):}`


If f(x) = `1/(1 - x)`, the number of points of discontinuity of f{f[f(x)]} is ______.


If the function f(x) = `[tan(π/4 + x)]^(1/x)` for x ≠ 0 is = K for x = 0 continuous at x = 0, then K = ?


If the function f(x) defined by

f(x) = `{{:(x sin  1/x",", "for"  x = 0),(k",", "for"  x = 0):}`

is continuous at x = 0, then k is equal to ______.


The function f(x) = x – |x – x2| is ______.


If f(x) = `{{:((x - 4)/(|x - 4|) + a",",  "for"  x < 4),(a + b",",  "for"  x = 4  "is continuous at"  x = 4","),((x - 4)/(|x - 4|) + b",",  "for"  x > 4):}`

then ______.


If f(x) = `{{:((3 sin πx)/(5x),",", x ≠ 0),(2k,",", x = 0):}`

is continuous at x = 0, then the value of k is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×