Advertisements
Advertisements
प्रश्न
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 ______.
विकल्प
0
– 1
1
None of these
Advertisements
उत्तर
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 0.
Explanation:
Given that: f(x) = `x^2 sin 1/x` where x ≠ 0
So, the value of the function f at x = 0
So that f(x) is continuous is 0.
APPEARS IN
संबंधित प्रश्न
Examine the following function for continuity:
f(x) = `1/(x - 5)`, x ≠ 5
Examine the following function for continuity:
f(x) = `(x^2 - 25)/(x + 5)`, x ≠ −5
Examine the following function for continuity:
f(x) = |x – 5|
A function f(x) is defined as,
Discuss the continuity of the following functions at the indicated point(s):
Discuss the continuity of the following functions at the indicated point(s):
Discuss the continuity of the following functions at the indicated point(s):
For what value of k is the function
\[f\left( x \right) = \begin{cases}\frac{\sin 5x}{3x}, if & x \neq 0 \\ k , if & x = 0\end{cases}\text{is continuous at x} = 0?\]
In each of the following, find the value of the constant k so that the given function is continuous at the indicated point;
Find the points of discontinuity, if any, of the following functions: \[f\left( x \right) = \begin{cases}\frac{x^4 + x^3 + 2 x^2}{\tan^{- 1} x}, & \text{ if } x \neq 0 \\ 10 , & \text{ if } x = 0\end{cases}\]
Discuss the continuity of the function \[f\left( x \right) = \begin{cases}2x - 1 , & \text { if } x < 2 \\ \frac{3x}{2} , & \text{ if } x \geq 2\end{cases}\]
Determine if \[f\left( x \right) = \begin{cases}x^2 \sin\frac{1}{x} , & x \neq 0 \\ 0 , & x = 0\end{cases}\] is a continuous function?
If \[f\left( x \right) = \begin{cases}\frac{{36}^x - 9^x - 4^x + 1}{\sqrt{2} - \sqrt{1 + \cos x}}, & x \neq 0 \\ k , & x = 0\end{cases}\]is continuous at x = 0, then k equals
Let f (x) = | x | + | x − 1|, then
If \[f\left( x \right) = \begin{cases}mx + 1 , & x \leq \frac{\pi}{2} \\ \sin x + n, & x > \frac{\pi}{2}\end{cases}\] is continuous at \[x = \frac{\pi}{2}\] , then
The value of f (0), so that the function
The value of b for which the function
If \[f\left( x \right) = \left\{ \begin{array}a x^2 + b , & 0 \leq x < 1 \\ 4 , & x = 1 \\ x + 3 , & 1 < x \leq 2\end{array}, \right.\] then the value of (a, b) for which f (x) cannot be continuous at x = 1, is
The values of the constants a, b and c for which the function \[f\left( x \right) = \begin{cases}\left( 1 + ax \right)^{1/x} , & x < 0 \\ b , & x = 0 \\ \frac{\left( x + c \right)^{1/3} - 1}{\left( x + 1 \right)^{1/2} - 1}, & x > 0\end{cases}\] may be continuous at x = 0, are
If \[f\left( x \right) = \begin{cases}\frac{1 - \sin^2 x}{3 \cos^2 x} , & x < \frac{\pi}{2} \\ a , & x = \frac{\pi}{2} \\ \frac{b\left( 1 - \sin x \right)}{\left( \pi - 2x \right)^2}, & x > \frac{\pi}{2}\end{cases}\]. Then, f (x) is continuous at \[x = \frac{\pi}{2}\], if
Write the number of points where f (x) = |x| + |x − 1| is continuous but not differentiable.
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`
If f is continuous at x = 0 then find f(0) where f(x) = `[5^x + 5^-x - 2]/x^2`, x ≠ 0
Discuss the continuity of the function f at x = 0
If f(x) = `(2^(3x) - 1)/tanx`, for x ≠ 0
= 1, for x = 0
Discuss the continuity of function f at x = 0.
Where f(X) = `[ [sqrt ( 4 + x ) - 2 ]/ ( 3x )]`, For x ≠ 0
= `1/12`, For x = 0
The probability distribution function of continuous random variable X is given by
f( x ) = `x/4`, 0 < x < 2
= 0, Otherwise
Find P( x ≤ 1)
Find the value of the constant k so that the function f defined below is continuous at x = 0, where f(x) = `{{:((1 - cos4x)/(8x^2)",", x ≠ 0),("k"",", x = 0):}`
Discuss the continuity of the function f(x) = sin x . cos x.
Show that the function f defined by f(x) = `{{:(x sin 1/x",", x ≠ 0),(0",", x = 0):}` is continuous at x = 0.
The function given by f (x) = tanx is discontinuous on the set ______.
f(x) = `{{:(|x|cos 1/x",", "if" x ≠ 0),(0",", "if" x = 0):}` at x = 0
Find the values of a and b such that the function f defined by
f(x) = `{{:((x - 4)/(|x - 4|) + "a"",", "if" x < 4),("a" + "b"",", "if" x = 4),((x - 4)/(|x - 4|) + "b"",", "if" x > 4):}`
is a continuous function at x = 4.
Given the function f(x) = `1/(x + 2)`. Find the points of discontinuity of the composite function y = f(f(x))
Examine the differentiability of f, where f is defined by
f(x) = `{{:(1 + x",", "if" x ≤ 2),(5 - x",", "if" x > 2):}` at x = 2
The set of points where the function f given by f(x) = |2x − 1| sinx is differentiable is ______.
