Limx- 3-x-x- is where - denotes the greatest integer function

L.H.L.=lim_x→ 3^ ([x]+[ x]) =2+( 3)= 1 (∵ x→ 3^ ⇒ x is in left side of 3) R.H.L.=lim_x→ 3^+([x]+[ x]) =3+( 4)= 1 (∵ x→ 3^+ ⇒ x is in right side of 3) So, L ...

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

Byju's Answer

Standard XII

Mathematics

Range

limx→ 3[x]+[-...

Question

$lim x \to 3 ([x] + [- x])$ is $($ where $[.]$ denotes the greatest integer function $)$

0

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

1

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

- 1

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

not defined

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

Open in App

Solution

The correct option is C $- 1$
$L . H . L . = lim x \to 3^{-} ([x] + [- x]) = 2 + (- 3) = - 1$
$(∵ x \to 3^{-} \Rightarrow x$ is in left side of $3)$

$R . H . L . = lim x \to 3^{+} ([x] + [- x]) = 3 + (- 4) = - 1$
$(∵ x \to 3^{+} \Rightarrow x$ is in right side of $3)$

So, $L . H . L . = R . H . L . = - 1$
$∴ lim x \to 3 ([x] + [- x]) = - 1$

Suggest Corrections

Similar questions

Q. The area bounded by the curves

y = x^{2}

and

y = \frac{2}{1 + x^{2}}

λ

sq. units. Then the value of

[λ]

(

where

[.]

denotes the greatest integer function

)

Q. If

{⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & a 0 & 1 & 4 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦}^{n} = ⎡ ⎢ ⎣ \begin{matrix} 1 & 18 & 2007 0 & 1 & 36 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦

(

where

[.]

denotes the greatest integer function and

n \in N),

then the value of

[\frac{n + a}{100}]

f (x) = ([x] + [- x]), x \neq 3

is continuous at

x = 3,

then the value of

f (3)

(

where

[.]

denotes the greatest integer function

)

Q. The integral

1 / 2 \int - 1 / 2 {[x] + log (\frac{1 + x}{1 - x})} d x

is equal to

(

where

[\cdot]

represents greatest integer function

)

m a x {x - [x], - x + [x]}; [] = G r e a t e s t i n t e g e r f u n c t i o n .

Join BYJU'S Learning Program

Explore more

Range

Standard XII Mathematics

Join BYJU'S Learning Program

limx→3([x]+[−x]) is (where [.] denotes the greatest integer function)

The correct option is C −1L.H.L.=limx→3−([x]+[−x])=2+(−3)=−1 (∵x→3−⇒x is in left side of 3) R.H.L.=limx→3+([x]+[−x])=3+(−4)=−1 (∵x→3+⇒x is in right side of 3) So, L.H.L.=R.H.L.=−1 ∴limx→3([x]+[−x])=−1

$lim x \to 3 ([x] + [- x])$ is $($ where $[.]$ denotes the greatest integer function $)$