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प्रश्न
Choose the correct alternative:
The value of `lim_(x -> "k") x - [x]`, where k is an integer is
पर्याय
– 1
1
0
2
उत्तर
1
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संबंधित प्रश्न
Examine the continuity of the following:
e2x + x2
Examine the continuity of the following:
x . log x
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 + 2",", "if", x ≥ 2),(x^2",", "if", x < 2):}`
Find the points of discontinuity of the function f, where `f(x) = {{:(x^3 - 3",", "if" x ≤ 2),(x^2 + 1",", "if" x < 2):}`
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):}`
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) = {{:((x - 1)^3",", "if" x < 0),((x + 1)^3",", "if" x ≥ 0):}`
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) = (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:
At x = `3/2` the function f(x) = `|2x - 3|/(2x - 3)` 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
