Limits

Question 1

Direct Substitution

Answer 1

Plug in the limit number for x (Only works if outcome isn’t infinity or 0/0)

Question 2

Factoring

Answer 2

See if factoring can cancel out a term (then use direct substitution)

Question 3

Rationalizing

Answer 3

Multiply numerator and denominator by conjugate (then see if you can factor or use direct substitution without getting DNE)

Question 4

FEPL

Answer 4

Use if limit reaches infinity:
(fastest) Factorial –> Exponential –> Polynomial –> Logarithmic (slowest)
Slower/faster = 0
Faster/slower = DNE

Question 5

WMM (what matters most)

Answer 5

Take the leading terms for the denominator and numerator and divide

Question 6

Your answer is:
infinity - infinity

Answer 6

Keep using methods to solve for an answer

Question 7

Graphs (continuous vs discontinuous)

Answer 7

Removable = holes
Non-removable = jumps and vertical asymptotes

Question 8

f(x) vs f ‘(x) vs f ‘‘(x)

Answer 8

f(x) = above/below/on the x-axis
f ‘(x) = slope/tangent lines
f ‘‘(x) = concavity