Advertisements
Advertisements
प्रश्न
The number of points at which the function f(x) = `1/(log|x|)` is discontinuous is ______.
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
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):}`
If \[f\left( x \right) = \begin{cases}\frac{\sin 3x}{x}, when & x \neq 0 \\ 1 , when & x = 0\end{cases}\]
Find whether f(x) is continuous at x = 0.
Discuss the continuity of the following functions at the indicated point(s):
(ii) \[f\left( x \right) = \left\{ \begin{array}{l}x^2 \sin\left( \frac{1}{x} \right), & x \neq 0 \\ 0 , & x = 0\end{array}at x = 0 \right.\]
Discuss the continuity of the following functions at the indicated point(s): (iv) \[f\left( x \right) = \left\{ \begin{array}{l}\frac{e^x - 1}{\log(1 + 2x)}, if & x \neq a \\ 7 , if & x = 0\end{array}at x = 0 \right.\]
Discuss the continuity of the following functions at the indicated point(s):
Determine the value of the constant k so that the function
\[f\left( x \right) = \begin{cases}k x^2 , if & x \leq 2 \\ 3 , if & x > 2\end{cases}\text{is continuous at x} = 2 .\]
Find the value of k for which \[f\left( x \right) = \begin{cases}\frac{1 - \cos 4x}{8 x^2}, \text{ when} & x \neq 0 \\ k ,\text{ when } & x = 0\end{cases}\] is continuous at x = 0;
In each of the following, find the value of the constant k so that the given function is continuous at the indicated point; \[f\left( x \right) = \begin{cases}\frac{x^2 - 25}{x - 5}, & x \neq 5 \\ k , & x = 5\end{cases}\]at x = 5
Find all the points of discontinuity of f defined by f (x) = | x |− | x + 1 |.
Find all point of discontinuity of the function
If \[f\left( x \right) = \left| \log_{10} x \right|\] then at x = 1
If \[f\left( x \right) = \begin{cases}\frac{\sin \left( \cos x \right) - \cos x}{\left( \pi - 2x \right)^2}, & x \neq \frac{\pi}{2} \\ k , & x = \frac{\pi}{2}\end{cases}\]is continuous at x = π/2, then k is equal to
Show that f(x) = |x − 2| is continuous but not differentiable at x = 2.
Discuss the continuity and differentiability of f (x) = |log |x||.
Write the number of points where f (x) = |x| + |x − 1| is continuous but not differentiable.
If f (x) = |3 − x| + (3 + x), where (x) denotes the least integer greater than or equal to x, then f (x) 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
The set of points where the function f (x) given by f (x) = |x − 3| cos x is differentiable, is
Find whether the following function is differentiable at x = 1 and x = 2 or not : \[f\left( x \right) = \begin{cases}x, & & x < 1 \\ 2 - x, & & 1 \leq x \leq 2 \\ - 2 + 3x - x^2 , & & x > 2\end{cases}\] .
Find the value of k for which the function f (x ) = \[\binom{\frac{x^2 + 3x - 10}{x - 2}, x \neq 2}{ k , x^2 }\] is continuous at x = 2 .
Find `dy/dx if y = tan^-1 ((6x)/[ 1 - 5x^2])`
Discuss the continuity of the function at the point given. If the function is discontinuous, then remove the discontinuity.
f (x) = `(sin^2 5x)/x^2` for x ≠ 0
= 5 for x = 0, at x = 0
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 ______.
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) = `{{:((2^(x + 2) - 16)/(4^x - 16)",", "if" x ≠ 2),("k"",", "if" x = 2):}` at x = 2
Find the values of p and q so that f(x) = `{{:(x^2 + 3x + "p"",", "if" x ≤ 1),("q"x + 2",", "if" x > 1):}` is differentiable at x = 1
If f(x) = `x^2 sin 1/x` where x ≠ 0, then the value of the function f at x = 0, so that the function is continuous at x = 0, is ______.
If f is continuous on its domain D, then |f| is also continuous on D.
