Advertisements
Advertisements
प्रश्न
The number of points at which the function f(x) = `1/(log|x|)` is discontinuous is ______.
Advertisements
उत्तर
The number of points at which the function f(x) = `1/(log|x|)` is discontinuous is 3.
Explanation:
The given function is discontinuous at x = 0, ± 1 and hence the number of points of discontinuity is 3
APPEARS IN
संबंधित प्रश्न
Examine the following function for continuity:
f(x) = x – 5
Discuss the continuity of the function f, where f is defined by:
f(x) = `{(3", if" 0 <= x <= 1),(4", if" 1 < x < 3),(5", if" 3 <= x <= 10):}`
A function f(x) is defined as,
In each of the following, find the value of the constant k so that the given function is continuous at the indicated point; \[f\left( x \right) = \binom{\frac{x^3 + x^2 - 16x + 20}{\left( x - 2 \right)^2}, x \neq 2}{k, x = 2}\]
If the functions f(x), defined below is continuous at x = 0, find the value of k. \[f\left( x \right) = \begin{cases}\frac{1 - \cos 2x}{2 x^2}, & x < 0 \\ k , & x = 0 \\ \frac{x}{\left| x \right|} , & x > 0\end{cases}\]
Find the points of discontinuity, if any, of the following functions:
Find the values of a and b so that the function f(x) defined by \[f\left( x \right) = \begin{cases}x + a\sqrt{2}\sin x , & \text{ if }0 \leq x < \pi/4 \\ 2x \cot x + b , & \text{ if } \pi/4 \leq x < \pi/2 \\ a \cos 2x - b \sin x, & \text{ if } \pi/2 \leq x \leq \pi\end{cases}\]becomes continuous on [0, π].
Discuss the continuity of the function \[f\left( x \right) = \begin{cases}2x - 1 , & \text { if } x < 2 \\ \frac{3x}{2} , & \text{ if } x \geq 2\end{cases}\]
Write the value of b for which \[f\left( x \right) = \begin{cases}5x - 4 & 0 < x \leq 1 \\ 4 x^2 + 3bx & 1 < x < 2\end{cases}\] is continuous at x = 1.
The function
If \[f\left( x \right) = \frac{1}{1 - x}\] , then the set of points discontinuity of the function f (f(f(x))) is
The function \[f\left( x \right) = \frac{x^3 + x^2 - 16x + 20}{x - 2}\] is not defined for x = 2. In order to make f (x) continuous at x = 2, Here f (2) should be defined as ______.
Show that f(x) = x1/3 is not differentiable at x = 0.
Write an example of a function which is everywhere continuous but fails to differentiable exactly at five points.
Discuss the continuity and differentiability of f (x) = |log |x||.
Write the points where f (x) = |loge x| is not differentiable.
The function f (x) = sin−1 (cos x) is
The set of points where the function f (x) = x |x| is differentiable is
If \[f\left( x \right) = \begin{cases}\frac{1}{1 + e^{1/x}} & , x \neq 0 \\ 0 & , x = 0\end{cases}\] then f (x) is
Let \[f\left( x \right) = \begin{cases}1 , & x \leq - 1 \\ \left| x \right|, & - 1 < x < 1 \\ 0 , & x \geq 1\end{cases}\] Then, f is
Discuss continuity of f(x) =`(x^3-64)/(sqrt(x^2+9)-5)` For x ≠ 4
= 10 for x = 4 at x = 4
Evaluate :`int Sinx/(sqrt(cos^2 x-2 cos x-3)) dx`
Discuss the continuity of f at x = 1
Where f(X) = `[ 3 - sqrt ( 2x + 7 ) / ( x - 1 )]` For x ≠ 1
= `-1/3` For x = 1
Find k, if the function f is continuous at x = 0, where
`f(x)=[(e^x - 1)(sinx)]/x^2`, for x ≠ 0
= k , for x = 0
Examine the continuity of the following function :
f(x) = x2 - x + 9, for x ≤ 3
= 4x + 3, for x > 3
at x = 3.
Examine the continuity of the followin function :
`{:(,f(x),=x^2cos(1/x),",","for "x!=0),(,,=0,",","for "x=0):}}" at "x=0`
Discuss the continuity of the function `f(x) = (3 - sqrt(2x + 7))/(x - 1)` for x ≠ 1
= `-1/3` for x = 1, at x = 1
Show that the function f defined by f(x) = `{{:(x sin 1/x",", x ≠ 0),(0",", x = 0):}` is continuous at x = 0.
If f(x) = `(sqrt(2) cos x - 1)/(cot x - 1), x ≠ pi/4` find the value of `"f"(pi/4)` so that f (x) becomes continuous at x = `pi/4`
The function given by f (x) = tanx is discontinuous on the set ______.
The value of k which makes the function defined by f(x) = `{{:(sin 1/x",", "if" x ≠ 0),("k"",", "if" x = 0):}`, continuous at x = 0 is ______.
The set of points where the functions f given by f(x) = |x – 3| cosx is differentiable is ______.
Examine the continuity of the function f(x) = x3 + 2x2 – 1 at x = 1
f(x) = `{{:((1 - cos 2x)/x^2",", "if" x ≠ 0),(5",", "if" x = 0):}` at x = 0
f(x) = `{{:(x^2/2",", "if" 0 ≤ x ≤ 1),(2x^2 - 3x + 3/2",", "if" 1 < x ≤ 2):}` at x = 1
If f(x) = `{{:("m"x + 1",", "if" x ≤ pi/2),(sin x + "n"",", "If" x > pi/2):}`, is continuous at x = `pi/2`, then ______.
If f is continuous on its domain D, then |f| is also continuous on D.
If the following function is continuous at x = 2 then the value of k will be ______.
f(x) = `{{:(2x + 1",", if x < 2),( k",", if x = 2),(3x - 1",", if x > 2):}`
