Calculus
Limit Calculator
Evaluate limits as x approaches any value or infinity. Compute one-sided and two-sided limits, detect indeterminate forms, and apply L'Hôpital's rule automatically.
d/dx
Examples:
Differentiation Rules
Power Rule
d/dx [x^n] = nx^(n-1)
Product Rule
[fg]' = f'g + fg'
Chain Rule
d/dx [f(g(x))] = f'(g(x))g'(x)
Constant Rule
d/dx [c] = 0
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Solution Methodology
01
Enter Function & Point
Input f(x) and the limit point c (or ∞, −∞).
02
Try Direct Substitution
Substitute x = c; if determinate, return the result immediately.
03
Apply L'Hôpital or Simplify
For indeterminate forms, differentiate or algebraically simplify, then re-evaluate.
Common Questions
When is L'Hôpital's Rule applied?
L'Hôpital's Rule applies when a limit produces an indeterminate form 0/0 or ±∞/∞ after direct substitution. The rule states that lim f(x)/g(x) = lim f'(x)/g'(x), provided the derivatives exist and the new limit is determinate. It may be applied repeatedly if the result remains indeterminate.
How do you find the limit as x approaches infinity?
For rational functions, divide every term by the highest power of x in the denominator. Terms with x in the denominator vanish as x→∞, leaving only the ratio of leading coefficients. For other functions, identify the dominant term and apply known limits like lim(1/x)=0 or lim(eˣ/xⁿ)=∞.