If fx -x-x- find whether fx is continuous at x-0-

The correct option is B discontinuous at x=0From the graph of the functions f(x)=x|x| , we can see that function is continuous everywhere except at x ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Continuity of a Function

If fx =x|x|...

Question

If $f (x) = \frac{x}{| x |}$ , find whether f(x) is continuous at $x = 0$ .

continuous at x=0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

discontinuous at x=0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

does not exist at x=0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of the above

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B discontinuous at x=0
From the graph of the functions $f (x) = \frac{x}{| x |}$ , we can see that function is continuous everywhere except at $x = 0$ .
Because $[l i m_{x \to 0^{-}} = - 1] \neq [l i m_{x \to 0^{+}} = 1]$

Suggest Corrections

Similar questions

Q. If

f (x) = \{\begin{cases} e^{1 / x}, if & x \neq 0 \\ 1, if & x = 0 \end{cases}

find whether f is continuous at x = 0.

Q. Let f (x) = | x | + | x − 1|, then
(a) f (x) is continuous at x = 0, as well as at x = 1
(b) f (x) is continuous at x = 0, but not at x = 1
(c) f (x) is continuous at x = 1, but not at x = 0
(d) none of these

Q.
Let

f (x) = {\begin{matrix} x^{n} sin \frac{1}{x}, x \neq 0 0, x = 0 \end{matrix}

, then f(x) is continuous but not differentiable at x=0 if

\begin{matrix} f (x) = (1 + 2 x)^{1 / x}, & f o r & x \neq 0 = e^{2}, & f o r & x = 0 \end{matrix}}

x = 0

.Find whether

f (x)

is continuous or not

Q. Determine whether

f (x) = \{\begin{cases} \frac{\sin x^{2}}{x}, & x \neq 0 \\ 0, & x = 0 \end{cases}

is continuous at x = 0 or not.

Join BYJU'S Learning Program

If f(x)=x|x|, find whether f(x) is continuous at x=0.

The correct option is B discontinuous at x=0From the graph of the functions f(x)=x|x|, we can see that function is continuous everywhere except at x=0.Because [limx→0−=−1]≠[limx→0+=1]

If $f (x) = \frac{x}{| x |}$ , find whether f(x) is continuous at $x = 0$ .

The correct option is B discontinuous at x=0
From the graph of the functions $f (x) = \frac{x}{| x |}$ , we can see that function is continuous everywhere except at $x = 0$ .
Because $[l i m_{x \to 0^{-}} = - 1] \neq [l i m_{x \to 0^{+}} = 1]$