Advertisements
Advertisements
Question
State how continuity is destroyed at x = x0 for the following graphs.
Solution
The left-hand limit and right–hand limit does not coincide at x = x0
APPEARS IN
RELATED QUESTIONS
Examine the continuity of the following:
x + sin x
Examine the continuity of the following:
x2 cos x
Examine the continuity of the following:
e2x + x2
Examine the continuity of the following:
`|x - 2|/|x + 1|`
Find the points of discontinuity of the function f, where `f(x) = {{:(x^3 - 3",", "if" x ≤ 2),(x^2 + 1",", "if" x < 2):}`
At the given point x0 discover whether the given function is continuous or discontinuous citing the reasons for your answer:
x0 = 1, `f(x) = {{:((x^2 - 1)/(x - 1)",", x ≠ 1),(2",", x = 1):}`
At the given point x0 discover whether the given function is continuous or discontinuous citing the reasons for your answer:
x0 = 3, `f(x) = {{:((x^2 - 9)/(x - 3)",", "if" x ≠ 3),(5",", "if" x = 3):}`
Which of the following functions f has a removable discontinuity at x = x0? If the discontinuity is removable, find a function g that agrees with f for x ≠ x0 and is continuous on R.
`f(x) = (x^3 + 64)/(x + 4), x_0` = – 4
Which of the following functions f has a removable discontinuity at x = x0? If the discontinuity is removable, find a function g that agrees with f for x ≠ x0 and is continuous on R.
`f(x) = (3 - sqrt(x))/(9 - x), x_0` = 9
Find the constant b that makes g continuous on `(- oo, oo)`.
`g(x) = {{:(x^2 - "b"^2,"if" x < 4),("b"x + 20, "if" x ≥ 4):}`
The function `f(x) = (x^2 - 1)/(x^3 - 1)` is not defined at x = 1. What value must we give f(1) inorder to make f(x) continuous at x =1?
State how continuity is destroyed at x = x0 for the following graphs.
State how continuity is destroyed at x = x0 for the following graphs.
Choose the correct alternative:
Let the function f be defined by `f(x) = {{:(3x, 0 ≤ x ≤ 1),(-3 + 5, 1 < x ≤ 2):}`, then
Choose the correct alternative:
If f : R → R is defined by `f(x) = [x - 3] + |x - 4|` for x ∈ R then `lim_(x -> 3^-) f(x)` is equal to
Choose the correct alternative:
The value of `lim_(x -> "k") x - [x]`, where k is an integer is
Choose the correct alternative:
Let a function f be defined by `f(x) = (x - |x|)/x` for x ≠ 0 and f(0) = 2. Then f is
