Advertisements
Advertisements
प्रश्न
State how continuity is destroyed at x = x0 for the following graphs.
Advertisements
उत्तर
The limit of f(x) does not exist at x = x0
APPEARS IN
संबंधित प्रश्न
Prove that f(x) = 2x2 + 3x - 5 is continuous at all points in R
Examine the continuity of the following:
x2 cos x
Examine the continuity of the following:
ex tan x
Examine the continuity of the following:
x . log x
Examine the continuity of the following:
`(x^2 - 16)/(x + 4)`
Find the points of discontinuity of the function f, where `f(x) = {{:(sinx",", 0 ≤ x ≤ pi/4),(cos x",", pi/4 < x < pi/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):}`
Let `f(x) = {{:(0",", "if" x < 0),(x^2",", "if" 0 ≤ x ≤ 2),(4",", "if" x ≥ 2):}`. Graph the function. Show that f(x) continuous on `(- oo, oo)`
If f and g are continuous functions with f(3) = 5 and `lim_(x -> 3) [2f(x) - g(x)]` = 4, find g(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^2 - 2x - 8)/(x + 2), x_0` = – 2
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
Consider the function `f(x) = x sin pi/x`. What value must we give f(0) in order to make the function continuous everywhere?
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:
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:
At x = `3/2` the function f(x) = `|2x - 3|/(2x - 3)` is
Choose the correct alternative:
Let f : R → R be defined by `f(x) = {{:(x, x "is irrational"),(1 - x, x "is rational"):}` then f 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
