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Standard limits formulas
10 formulas for Standard limits, from the Calculus section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| sin x / x | lim(x→0) sin x / x = 1 | |
| tan x / x | lim(x→0) tan x / x = 1 | |
| (1 − cos x) / x² | lim(x→0) = ½ | |
| (eˣ − 1) / x | lim(x→0) = 1 | |
| (aˣ − 1) / x | lim(x→0) = ln a | |
| ln(1 + x) / x | lim(x→0) = 1 | |
| (xⁿ − aⁿ) / (x − a) | lim(x→a) = n·aⁿ⁻¹ | |
| e definition | lim(x→0) (1 + x)^(1/x) = e; lim(n→∞) (1 + 1/n)ⁿ = e | |
| 1^∞ form | lim f^g = e^(lim g(f − 1)) | |
| L'Hôpital's rule | lim f/g = lim f′/g′ | 0/0 or ∞/∞ forms |
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