Limits And Continuity
Telangana Open School (TOSS) · Class 12 · Mathematics
All formulas from Limits And Continuity in Telangana Open School (TOSS) Class 12 Mathematics. Key equations, constants, and identities for board exam preparation.
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Formulas
Algebraic Limits
limₓ→ₐ (xⁿ − aⁿ)/(x − a) = n aⁿ⁻¹
limₓ→ₐ (xᵐ − aᵐ)/(xⁿ − aⁿ) = (m/n) aᵐ⁻ⁿ
limₓ→₀ (eˣ − 1)/x = 1
limₓ→₀ (aˣ − 1)/x = logₑ a
Trigonometric Limits
limₓ→₀ sin x / x = 1
limₓ→₀ tan x / x = 1
limₓ→₀ (1 − cos x)/x² = 1/2
limₓ→ₐ sin(x − a)/(x − a) = 1
Exponential and Logarithmic Limits
limₓ→₀ (1 + x)¹/ˣ = e
limₓ→∞ (1 + 1/x)ˣ = e
limₓ→₀ log(1 + x)/x = 1
limₓ→₀ (e^λˣ − 1)/x = λ
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