हिंदी

Examine the continuity of f(x) = x3 + 2x2 − x − 2 at x = − 2 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Examine the continuity of f(x) = x3 + 2x2 − x − 2 at x = − 2

योग

उत्तर

Every polynomial is continuous for all values of x f(x) = x3 + 2x2 − x − 2 is a polynomial and hence continuous at x = − 2.

shaalaa.com
Continuous and Discontinuous Functions
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 8: Continuity - EXERCISE 8.1 [पृष्ठ १७२]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
अध्याय 8 Continuity
EXERCISE 8.1 | Q 1) (i) | पृष्ठ १७२

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 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 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`


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

f(x) = `(x^2 - 10x + 21)/(x - 7)`


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

f(x) `{:(= x^2 + 3x - 2",",  "for"  x ≤ 4),(= 5x + 3",",  "for"  x > 4):}`


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) = `(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) = `{:(=( sqrt(3) - tanx)/(pi - 3x)",", x ≠ pi/3),(= 3/4",", x = pi/3):}}  "at"  x = pi/3`


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):}`


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


If f(x)  `{:(= (5^x + 5^(-x) - 2)/(x^2)"," , "for"  x ≠ 0),(= k",",  "for"  x = 0):}}` is continuous at x = 0, find k


For what values of a and b is the function

f(x) `{:(= (x^2 - 4)/(x - 2)",", "for"  x < 2),(= "a"x^2 - "b"x + 3",", "for"  2 ≤ x < 3),(= 2x - "a" + "b"",", "for"  x ≥ 3):}}` continuous for every x on R?


Determine the values of p and q such that the following function is continuous on the entire real number line.

f(x) `{:(= x + 1",", "for"   1 < x < 3),(= x^2 + "p"x + "q"",", "for"  |x - 2| ≥ 1):}`


Show that there is a root for the equation 2x3 − x − 16 = 0 between 2 and 3.


Let f(x) = ax + b (where a and b are unknown)

= x2 + 5 for x ∈ R

Find the values of a and b, so that f(x) is continuous at x = 1


Suppose f(x) `{:(= "p"x + 3",", "for"  "a" ≤ x ≤ "b"),(= 5x^2 − "q"",", "for"  "b" < x ≤ "c"):}`

Find the condition on p, q, so that f(x) is continuous on [a, c], by filling in the blanks.

f(b) = ______

`lim_(x -> "b"^+) "f"(x)` = _______

∴ pb + 3 = _______ − q

∴ p = `"_____"/"b"` is the required condition


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) = `(x^2 - 7x + 10)/(x^2 + 2x - 8)`, for x ∈ [– 6, – 3]


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’ =


Select the correct answer from the given alternatives:

If f(x) = `((4 + 5x)/(4 - 7x))^(4/x)`, for x ≠ 0 and f(0) = k, is continuous at x = 0, then k is


Select the correct answer from the given alternatives:

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


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

f(x) `{:( = (sin^2pix)/(3(1 - x)^2) ",", "for"  x ≠ 1),(= (pi^2sin^2((pix)/2))/(3 + 4cos^2 ((pix)/2)) ",", "for"  x = 1):}}` at x = 1


Discuss the continuity of the following function at the point or on the interval indicated against them. If the function is discontinuous, identify the type of discontinuity and state whether the discontinuity is removable. If it has a removable discontinuity, redefine the function so that it becomes continuous:

f(x) = `((x + 3)(x^2 - 6x + 8))/(x^2 - x - 12)`


Find k if following function is continuous at the point indicated against them:

f(x) `{:(= ((5x - 8)/(8 - 3x))^(3/(2x - 4))",", "for"  x ≠ 2),(= "k"",", "for"  x = 2):}}` at x = 2


Find k if following function is continuous at the point indicated against them:

f(x) `{:(= (45^x - 9^x - 5^x + 1)/(("k"^x - 1)(3^x - 1))",", "for"  x ≠ 0),(= 2/3",", "for"  x = 0):}}` at 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


If f(x) = `{((x^4 - 1/81)/(x^3 - 1/27), x ≠ 1/3), (k, x = 1/3):}` is continuous at x = `1/3`, then the value of k is ______


If f(x) = `{:{(tan^-1|x|; "when"  x ≠ 0), (pi/4;  "when"  x = 0):}`, then ______ 


Let f : [-1, 2] → [0, ∞] be a continuous function such that f(x) = f(1 - x) ∀ x ∈ [-1, 2].

Let R1 = `int_-1^2 xf(x) dx` and R2 be the area of the region bounded by y = f(x), x = -1, x = 2 and the X-axis. Then, ______


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) = `1/(1 - x)`, the number of points of discontinuity of f{f[f(x)]} 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) = `{{:((sin^3(sqrt(3)).log(1  +  3x))/((tan^-1 sqrt(x))^2(e^(5sqrt(3))  -  1)x)",", x ≠ 0),(                         a",", x = 0):}`

is continuous in [0, 1] then a is equal to ______.


`lim_(x rightarrow 0) (e^(x^2) - cosx)/x^2` is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×