Advertisements
Advertisements
प्रश्न
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
पर्याय
`(f(3) + f(4.5))/7.5`
12
17.5
`(f(4.5) - f(3))/1.5`
उत्तर
`(f(4.5) - f(3))/1.5`
APPEARS IN
संबंधित प्रश्न
Examine the continuity of the following:
x2 cos x
Examine the continuity of the following:
ex tan x
Examine the continuity of the following:
e2x + x2
Examine the continuity of the following:
`(x^2 - 16)/(x + 4)`
Find the points of discontinuity of the function f, where `f(x) = {{:(4x + 5",", "if", x ≤ 3),(4x - 5",", "if", x > 3):}`
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):}`
Show that the function `{{:((x^3 - 1)/(x - 1)",", "if" x ≠ 1),(3",", "if" x = 1):}` is continuous om `(- oo, oo)`
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):}`
A function f is defined as follows:
`f(x) = {{:(0, "for" x < 0;),(x, "for" 0 ≤ x ≤ 1;),(- x^2 +4x - 2, "for" 1 ≤ x ≤ 3;),(4 - x, "for" x ≥ 3):}`
Is the function continuous?
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):}`
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.
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:
Let f : R → R be defined by `f(x) = {{:(x, x "is irrational"),(1 - x, x "is rational"):}` then f is
