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
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
Discuss the continuity of the function f, where f is defined by `f(x) = {(2x , ","if x < 0),(0, "," if 0 <= x <= 1),(4x, "," if x > 1):}`
Discuss the continuity of the following functions at the indicated point(s):
(i) \[f\left( x \right) = \begin{cases}\left| x \right| \cos\left( \frac{1}{x} \right), & x \neq 0 \\ 0 , & x = 0\end{cases}at x = 0\]
Discuss the continuity of the following functions at the indicated point(s):
Discuss the continuity of \[f\left( x \right) = \begin{cases}2x - 1 & , x < 0 \\ 2x + 1 & , x \geq 0\end{cases} at x = 0\]
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: \[f\left( x \right) = \begin{cases}\frac{\sin 3x}{x}, & \text{ if } x \neq 0 \\ 4 , & \text{ if } x = 0\end{cases}\]
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?
Find f (0), so that \[f\left( x \right) = \frac{x}{1 - \sqrt{1 - x}}\] becomes continuous at x = 0.
If \[f\left( x \right) = \begin{cases}\frac{x^2 - 16}{x - 4}, & \text{ if } x \neq 4 \\ k , & \text{ if } x = 4\end{cases}\] is continuous at x = 4, find k.
The value of b for which the function
Show that the function
\[f\left( x \right) = \begin{cases}\left| 2x - 3 \right| \left[ x \right], & x \geq 1 \\ \sin \left( \frac{\pi x}{2} \right), & x < 1\end{cases}\] is continuous but not differentiable at x = 1.
If f is defined by f (x) = x2, find f'(2).
Write an example of a function which is everywhere continuous but fails to differentiable exactly at five points.
Let f (x) = |x| and g (x) = |x3|, then
If \[f\left( x \right) = \left| \log_e |x| \right|\]
Discuss continuity of f(x) =`(x^3-64)/(sqrt(x^2+9)-5)` For x ≠ 4
= 10 for x = 4 at x = 4
Find the points of discontinuity , if any for the function : f(x) = `(x^2 - 9)/(sinx - 9)`
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
If Y = tan-1 `[(cos 2x - sin 2x)/(sin2x + cos 2x)]` then find `(dy)/(dx)`
If the function
f(x) = x2 + ax + b, x < 2
= 3x + 2, 2≤ x ≤ 4
= 2ax + 5b, 4 < x
is continuous at x = 2 and x = 4, then find the values of a and b
The function given by f (x) = tanx is discontinuous on the set ______.
A continuous function can have some points where limit does not exist.
Examine the continuity of the function f(x) = x3 + 2x2 – 1 at x = 1
f(x) = `{{:(|x - 4|/(2(x - 4))",", "if" x ≠ 4),(0",", "if" x = 4):}` at x = 4
f(x) = `{{:(("e"^(1/x))/(1 + "e"^(1/x))",", "if" x ≠ 0),(0",", "if" x = 0):}` at x = 0
Prove that the function f defined by
f(x) = `{{:(x/(|x| + 2x^2)",", x ≠ 0),("k", x = 0):}`
remains discontinuous at x = 0, regardless the choice of k.
An example of a function which is continuous everywhere but fails to be differentiable exactly at two points is ______.
The composition of two continuous function is a continuous function.
`lim_("x" -> "x" //4) ("cos x - sin x")/("x"- "x" /4)` is equal to ____________.