lim x → 3 − 1 − x x 1 [ x − 1 ] [ . ] → denotes greatest integer function

x − 3 ⇒ − x 1 < 3 ⇒ [ − 3 1 ] = 2 lim x → − 3 1 x 1 [ − x 1 ] = ( − 3 ) ( 2 ) = − 6

Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsGeneral ( Limit existence)Easy2 minQB

MathematicsEasysingle choice

$lim_{x \to \frac{- 1}{3} - x} \frac{1}{x} [\frac{- 1}{x}] [.] \to$ denotes greatest integer function

Answer:

Solution:

$x < - \frac{1}{3}$

$\frac{1}{x} > - 3 \Rightarrow - \frac{1}{x} < 3 \Rightarrow [- \frac{1}{3}] = 2$

$lim_{x \to - \frac{1}{3}} \frac{1}{x} [- \frac{1}{x}] = (- 3) (2) = - 6$

Stream:JEESubject:MathematicsTopic:LimitsSubtopic:General ( Limit existence)

⏱ 2mℹ️ Source: QB

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