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q1)fⁿa and gⁿa exist and are not equal for some n .
Further if f(a)g(x) - f(a) - g(a)f(x) +g(a) =4
g(x) - f(x)

then value of n is:

ans is 4 how??

lim ( 1+2⁴+3⁴+........n⁴ - lim 1+2³+3³+........n³ )
nâ†’âˆž n⁵

Q2)expansion of log(1+3x+2x² ) is:

#Mathematics #Calculus

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Dr.House ·2011-02-02 23:34:41

2) write it as

log[(1 + x + x2) / (1 - x + x2)]

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Vinay Arya ·2011-02-03 20:04:51

(2) 1+3x+2x²=2x²+3x+1=2x²+2x+x+1=2x(x+1)+(x+1)
=(2x+1)(x+1)
So log(2x²+3x+1)=log[(2x+1)(x+1)]=log(2x+1) +log(x+1)
=(1+2x+(2x)²2+...................âˆž)+(1+x+x^²2+.....................âˆž)
I hope that you can solve it from this point

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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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