Advertisements
Advertisements
प्रश्न
Find all points of discontinuity of f, where f is defined by `f (x) = {(x/|x|, if x<0),(-1, if x >= 0):}`
उत्तर
`f (x) = {(x/|x|, if x<0),(-1, if x >= 0):}`
`lim_(x -> 0^-) f(x) = lim_(x -> 0^-) x/abs x`
= `lim_(h -> 0) ((0 - h))/ abs (0 - h)`
`= lim_(h -> 0) (-h)/h = - 1`
`lim_(x -> 0^+)` f(x) = -1
f(0) = - 1
Hence, f is continuous at x = 0.
There are no points of discontinuity here.
APPEARS IN
संबंधित प्रश्न
Discuss the continuity of the following functions. If the function have a removable discontinuity, redefine the function so as to remove the discontinuity
`f(x)=(4^x-e^x)/(6^x-1)` for x ≠ 0
`=log(2/3) ` for x=0
Show that the function `f(x)=|x-3|,x in R` is continuous but not differentiable at x = 3.
Examine the continuity of the function f(x) = 2x2 – 1 at x = 3.
Find all point of discontinuity of f, where f is defined by `f (x) = {(2x + 3, if x<=2),(2x - 3, if x > 2):}`
Find all points of discontinuity of f, where f is defined by `f(x) = {(|x|+3, if x<= -3),(-2x, if -3 < x < 3),(6x + 2, if x >= 3):}`
Find all points of discontinuity of f, where f is defined by `f(x) = {(x^3 - 3, if x <= 2),(x^2 + 1, if x > 2):}`
Find the points of discontinuity of f, where `f (x) = {(sinx/x, if x<0),(x + 1, if x >= 0):}`
Determine if f defined by `f(x) = {(x^2 sin 1/x, "," if x != 0),(0, "," if x = 0):}` is a continuous function?
Examine the continuity of f, where f is defined by `f(x) = {(sin x - cos x, if x != 0),(-1, "," if x = 0):}`
Find all the points of discontinuity of f defined by `f(x) = |x| - |x + 1|`.
Determine the value of the constant 'k' so that function f(x) `{((kx)/|x|, ","if x < 0),(3"," , if x >= 0):}` is continuous at x = 0
Test the continuity of the function on f(x) at the origin:
\[f\left( x \right) = \begin{cases}\frac{x}{\left| x \right|}, & x \neq 0 \\ 1 , & x = 0\end{cases}\]
Find the points of discontinuity, if any, of the following functions: \[f\left( x \right) = \begin{cases}2x , & \text{ if } & x < 0 \\ 0 , & \text{ if } & 0 \leq x \leq 1 \\ 4x , & \text{ if } & x > 1\end{cases}\]
The function f (x) = tan x is discontinuous on the set
Find the point of discontinuity, if any, of the following function: \[f\left( x \right) = \begin{cases}\sin x - \cos x , & \text{ if } x \neq 0 \\ - 1 , & \text{ if } x = 0\end{cases}\]
Show that the function `f(x) = |x-4|, x ∈ R` is continuous, but not diffrent at x = 4.
Prove that `1/2 "cos"^(-1) ((1-"x")/(1+"x")) = "tan"^-1 sqrt"x"`
Find all points of discontinuity of the function f(t) = `1/("t"^2 + "t" - 2)`, where t = `1/(x - 1)`
`lim_("x" -> pi/2)` [sinx] is equal to ____________.
The number of discontinuous functions y(x) on [-2, 2] satisfying x2 + y2 = 4 is ____________.
Let f (x) `= (1 - "tan x")/(4"x" - pi), "x" ne pi/4, "x" in (0, pi/2).` If f(x) is continuous in `(0, pi/2), "then f"(pi/4) =` ____________.
`lim_("x"-> 0) sqrt(1/2 (1 - "cos" 2"x"))/"x"` is equal to
The domain of the function f(x) = `""^(24 - x)C_(3x - 1) + ""^(40 - 6x)C_(8x - 10)` is
The function f defined by `f(x) = {{:(x, "if" x ≤ 1),(5, "if" x > 1):}` discontinuous at x equal to
The point of discountinuity of the function `f(x) = {{:(2x + 3",", x ≤ 2),(2x - 3",", x > 2):}` is are
How many point of discontinuity for the following function in its. domain.
`f(x) = {{:(x/|x|",", if x < 0),(-1",", if x ≥ 0):}`
How many point of discontinuity for the following function for x ∈ R
`f(x) = {{:(x + 1",", if x ≥ 1),(x^2 + 1",", if x < 1):}`
`f(x) = {{:(x^10 - 1",", if x ≤ 1),(x^2",", if x > 1):}` is discontinuous at
Sin |x| is a continuous function for
Let a, b ∈ R, b ≠ 0. Define a function
F(x) = `{{:(asin π/2(x - 1)",", "for" x ≤ 0),((tan2x - sin2x)/(bx^3)",", "for" x > 0):}`
If f is continuous at x = 0, then 10 – ab is equal to ______.
If the function f defined as f(x) = `1/x - (k - 1)/(e^(2x) - 1)` x ≠ 0, is continuous at x = 0, then the ordered pair (k, f(0)) is equal to ______.
Consider the graph `y = x^(1/3)`
Statement 1: The above graph is continuous at x = 0
Statement 2: The above graph is differentiable at x = 0
Which of the following is correct?
