Test:20 QNo:2

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lim-x→0 (tanx-sinx)/x³=

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sahil jain ·2010-10-05 05:50:24

ans is 16.

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nihal raj ·2010-10-05 07:18:38

ANS IS 1/2

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BODO ·2010-10-05 11:10:22

of corse its 1/2

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Joydoot ghatak ·2010-10-05 21:07:53

yes the answer is 1/2.

let I = lim _xâ†’0 (tan x - sin x)/ x³.
= lim_xâ†’0 ( x + 1/3 x³ +2/15 x⁵.......) - (x -1/6 x³ +1/120 x⁵) / x³
{by applying expansion.}
=lim_xâ†’0 1/2 x³ + 17/120 x⁵......./ x³
=lim_xâ†’0 1/2 + 17/120 x²......
= 1/2.

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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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Test:20 QNo:2

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