Math 221 Exam 1 – Study Guide, Practice Problems & Exam Review
sum law lim as x→a [f(x) + g(x)] - ANS ✔✔lim f(x) as x→a + g(x) as x→a
difference law lim as x→a [f(x) - g(x)] - ANS ✔✔lim f(x) as x→a - g(x) as x→a
constant multiple law, lim as x→a [Cf(x)] - ANS ✔✔C*lim f(x) as x→a
product law, lim x→a [f(x) * g(x)] - ANS ✔✔lim f(x) as x→a * g(x) as x→a
quotient law, x→a f(x)/g(x) - ANS ✔✔lim f(x) as x→a / g(x) as x→a
power law, lim as x→a x^n = - ANS ✔✔a^n
root law, lim as x→a n√x = - ANS ✔✔n√a
how to solve limits with square roots - ANS ✔✔multiply by the conjugate
how to solve limits with absolute values - ANS ✔✔break into one sided limits
squeeze therom - ANS ✔✔-1 ≤ base function ≤1, multiple each part of the function by each
section. if they equal the same the main function must be the same as well
function f is continous at a number a if.. - ANS ✔✔lim f(x) as x approaches a = f(a)
Continuity definition implies which 3 things are true? - ANS ✔✔1. f(a) is defined (is a number)
sum law lim as x→a [f(x) + g(x)] - ANS ✔✔lim f(x) as x→a + g(x) as x→a
difference law lim as x→a [f(x) - g(x)] - ANS ✔✔lim f(x) as x→a - g(x) as x→a
constant multiple law, lim as x→a [Cf(x)] - ANS ✔✔C*lim f(x) as x→a
product law, lim x→a [f(x) * g(x)] - ANS ✔✔lim f(x) as x→a * g(x) as x→a
quotient law, x→a f(x)/g(x) - ANS ✔✔lim f(x) as x→a / g(x) as x→a
power law, lim as x→a x^n = - ANS ✔✔a^n
root law, lim as x→a n√x = - ANS ✔✔n√a
how to solve limits with square roots - ANS ✔✔multiply by the conjugate
how to solve limits with absolute values - ANS ✔✔break into one sided limits
squeeze therom - ANS ✔✔-1 ≤ base function ≤1, multiple each part of the function by each
section. if they equal the same the main function must be the same as well
function f is continous at a number a if.. - ANS ✔✔lim f(x) as x approaches a = f(a)
Continuity definition implies which 3 things are true? - ANS ✔✔1. f(a) is defined (is a number)
