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Formulas
L'Hôpital's Rule
Use when direct substitution gives 0/0 or ∞/∞.
Power Integral
Works for all n ≠ −1. For n = −1: ∫(1/x)dx = ln|x| + C.
Exponential Integral
Divide by the coefficient of x in the exponent.
Integration by Parts
Choose u as the factor that gets simpler when differentiated (logs, polynomials).
Hessian Determinant
|H|>0 + fxx<0 → max; |H|>0 + fxx>0 → min; |H|<0 → saddle point.
Part 1 of 1
Plugging in x = a gives 0/0 or ∞/∞. That's not the answer — it means you're stuck. L'Hôpital says: differentiate numerator and denominator separately, then try again.
Keep applying until the form resolves. ⚡ Exam callout: any 0/0 or ∞/∞ in a limit → reach for this immediately.
Worked example
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