Test:351 QNo:41

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The function f(x)=(x-sinx)/x³ is continuous at x=0, then f(0) is

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3 Answers

Saket Shukla ·2009-04-24 08:20:41

The explanation to the above question has been given as :
lim(xâ†’0)f(x)=f(0)

Applying LH rule (1-cosx)/2x²=sin²(x/2)/x²=1/4

However I solved it in the following way:

Applying LH rule 3 times= (1-cosx)/3x²= sinx/6x=cosx/6

hence lim(xâ†’0)cosx/6=1/6

Could you please tell me what's wrong in this?

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Mani Pal Singh ·2009-04-24 08:27:10

This have to done by the following method
Use the expansion of Sin x =x-x³/3!..........

=+1/6

so ur answer is correct

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Manish Shankar ·2009-04-24 08:29:53

you are absolutely right saket

there is a mistake in the solution
Applying LH rule (1-cosx)/2x2=sin2(x/2)/x2=1/4
instead of this it should have been
Applying LH rule (1-cosx)/3x2=2sin²(x/2)/3x²=1/6

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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:351 QNo:41

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