limits simple one but doubtful

IIT JEE 2015 Discussion Forum › Calculus questions › limits simple one but doubtful

Q- lim [ -2xtanx ]

xâ†’ 0

where [.]=greatest integer function.

why isn't the answer -3 ???

ans given is -2

i'm confused at this......

as xâ†’0 tanx/x â†’1
so xâ†’0 x/tanx â†’1+

but buk says

as xâ†’0
x/tanx < 1

#Mathematics #Calculus

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2 Answers

262

Aditya Bhutra ·2011-07-10 05:57:38

we know tanx/x >1 for x â†’0
[we can prove it by diff.]
therefore xtanx <1
-2xtanx >-2 (change in sign is due to multiplication with a -ve no.)
taking greatest integer func. ,

[-2xtanx] =-2

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rishabh ·2011-07-10 10:42:14

remember
tan x is always greater than x .

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Basic Integral Calculus Operators Symbols Matrix Cases

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω

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limits simple one but doubtful

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