Calc tests

Question 1

nth term test

Answer 1

if limit of equation as variable approaches infinity equals 0, it might be convergent. If not equal to 0, definitely diverges.

Question 2

integral test

Answer 2

if function is:
a) decreasing
b) continuous
c) positive
then if integral of f(x) converges, summation of f(x) converges

Question 3

comparison test

Answer 3

if f(x) is less than 1/x^0.5 or similar converging integral, f(x) converges

if f(x) is larger than 1/x^2 or similar diverging integral, f(x) diverges

ALWAYS say p = 0.5 < 1 or p = 2 > 1 in proof

Question 4

limit comparison test

Answer 4

b = leading term of n/leading term of d

if lim f(x)/b is finite and positive
then if b converges, f(x) also converges
but if b diverges, from f(x) also diverges

Question 5

ratio test

Answer 5

lim |f(x)/f(x+1)| = L
if L > 1, diverges
if L < 1, converges
inconclusive if = 0

Question 6

Alternating test

Answer 6

coverages if alternating, decreasing in magnitude, and passes nth term test