Limit Laws Practice Problems
These problems follow the limit laws lesson. Each one can be solved with the rules of limits and direct substitution, apart from the last few, which test when a law can’t be used.
The laws in one line each
- Sum and difference: the limit of
is . - Constant multiple and product: constants factor out, and the limit of
is . - Quotient: the limit of
is , only if . - Power and root: limits pass through powers and roots, as long as the root is defined.
Common mistakes to watch for
- Using the quotient law when the bottom goes to 0. Check the denominator limit first.
- Reading
as an answer. Simplify, then substitute again. - Splitting limits that do not exist. Each piece needs a limit for the laws to apply.
- Forgetting the root law needs a defined root. An even root needs a non-negative inside.