doomath Calculator
Limits & Asymptotic Analysis Calculator
Evaluate algebraic and rational limits x → c, detect 0/0 indeterminate forms, apply factoring or L'Hôpital's rule, and inspect left/right limits.
InputsChange a value to recalculate instantly
ResultUpdates as you type
FORMULA & STEPSLimits & Asymptotic Analysis Calculator — Mathematical Derivation & Steps
2 StepsSequential Calculation Breakdown
1
Substitute x = c
Check the direct form first.
2
Resolve 0/0
Direct substitution or divergent behavior determines the result.
λ DooMathWork with this calculation
Local · deterministic · optionalQuick mathNatural-language-style shortcuts for deterministic arithmetic.
Calculator guide
How to use the Limits & Asymptotic Analysis Calculator
Evaluate algebraic and rational limits x → c, detect 0/0 indeterminate forms, apply factoring or L'Hôpital's rule, and inspect left/right limits.
01Set inputsChoose values, units and assumptions.
02Apply the modellim_{x→c} [P(x) / Q(x)]; If [0/0], apply L'Hôpital: lim_{x→c} [P'(x) / Q'(x)]
03Read the resultCheck the output against the assumptions before using it.
What this calculator does
Specify the polynomial terms for numerator and denominator, plus the target limit point c. The solver detects indeterminate forms and applies calculus rules.
Formula & method
lim_{x→c} [P(x) / Q(x)]; If [0/0], apply L'Hôpital: lim_{x→c} [P'(x) / Q'(x)]
Assumptions & notes
- A limit exists if and only if both left-hand and right-hand limits exist and are equal.
- L'Hôpital's rule applies specifically to indeterminate forms [0/0] or [±∞/±∞].
- Direct substitution is the first test for continuity at x = c.