Advertisements
Advertisements
Question
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
Options
– 2
– 1
0
1
Advertisements
Solution
0
APPEARS IN
RELATED QUESTIONS
Prove that f(x) = 2x2 + 3x - 5 is continuous at all points in R
Examine the continuity of the following:
ex tan x
Examine the continuity of the following:
`sinx/x^2`
Examine the continuity of the following:
`(x^2 - 16)/(x + 4)`
Examine the continuity of the following:
|x + 2| + |x – 1|
Examine the continuity of the following:
cot x + tan 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) = {{:(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):}`
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?
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)`
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:
Let the function f be defined by `f(x) = {{:(3x, 0 ≤ x ≤ 1),(-3 + 5, 1 < x ≤ 2):}`, then
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
