LIMITS

Ques1) The value of lim xâ†’0 { cos (m²+n²) x } ^{mn / (m²+n²)x}
(a) e^mn^(m²+n²)
(b) e^{- mn}^(m²+n²)
(c) e^{- mn/2}^(m²+n²)
(d) e^mn/2^(m²+n²)

Ques2) lim xâ†’0 [sin^-1 x / tan ^-1 x ] , whre [.] denotes the greates integer function
(a)0 (b) 1 (c) -1 (d) n.d

Ques3) lim xâ†’âˆž (x³/( 3x²-4) - x² / 3x+2 )
(a) does not exists (b) 1/3 (c)0 (d) 2/9

2 Answers

q1
hint=http://www.targetiit.com/iit-jee-forum/posts/limits-11139.html

q2
check rhl and lhl
i think its d

q3
answer is c

divide by x² in num and den for 1st term
and
divide by x in num and den for 2nd term

2nd Answer as (d)
3) is (c)
1) is (c)

√ √ || {} [] () → ~ ^ 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