Advertisements
Advertisements
प्रश्न
Consider the function `f(x) = x sin pi/x`. What value must we give f(0) in order to make the function continuous everywhere?
उत्तर
`f(x) = x sin pi/x`
Define f(x) on R as
`f(x) = {{:(x sin pi/x, "if" x ≠ 0),(0, "if" x = 0):}`
∴ f(0) = 0.
Then f(x) is continuous on R.
APPEARS IN
संबंधित प्रश्न
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 . log x
Examine the continuity of the following:
|x + 2| + |x – 1|
Find the points of discontinuity of the function f, where `f(x) = {{:(x + 2",", "if", x ≥ 2),(x^2",", "if", x < 2):}`
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):}`
Show that the function `{{:((x^3 - 1)/(x - 1)",", "if" x ≠ 1),(3",", "if" x = 1):}` is continuous om `(- oo, oo)`
For what value of `alpha` is this function `f(x) = {{:((x^4 - 1)/(x - 1)",", "if" x ≠ 1),(alpha",", "if" x = 1):}` continuous at x = 1?
If f and g are continuous functions with f(3) = 5 and `lim_(x -> 3) [2f(x) - g(x)]` = 4, find g(3)
Find the points at which f is discontinuous. At which of these points f is continuous from the right, from the left, or neither? Sketch the graph of f.
`f(x) = {{:(2x + 1",", "if" x ≤ - 1),(3x",", "if" - 1 < x < 1),(2x - 1",", "if" x ≥ 1):}`
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):}`
State how continuity is destroyed at x = x0 for the following graphs.
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 f be a continuous function on [2, 5]. If f takes only rational values for all x and f(3) = 12, then f(4.5) is equal to
