lim x → 0 [ x ∣ s i n − 1 ∣ x ∣∣ ] (where [.] denotes greatest integer function) is

L H L = lim h → 0 [ h ∣ s i n − 1 h ∣ ] = lim h → 0 [ − h s i n − 1 h ] = − 2 R H L = h → 0 [ h sin − 1 h ] = 1

Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsGeneral ( Limit existence)Easy2 minQB

MathematicsEasymultiple choice

$lim_{x \to 0} [\frac{∣ s i n ^{- 1} ∣ x ∣∣}{x}]$ (where [.] denotes greatest integer function) is

Answer:

A,C

Solution:

$L H L = lim_{h \to 0} [\frac{∣ s i n ^{- 1} h ∣}{h}] = lim_{h \to 0} [\frac{s i n ^{- 1} h}{- h}] = - 2$

$R H L = h \to 0 [\frac{sin ^{- 1} h}{h}] = 1$

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

⏱ 2mℹ️ Source: QB

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