Test 2

Question 1

Conditions for a series to be tested with a test other than L.C.T.

Answer 1

Sequence must be: Decreasing, Continuous, Positive

Question 2

Test for divergence

Answer 2

If the sequence doesn’t converge, neither does the series
If the sequence does converge, then we still don’t know if the sequence converges

Question 3

p test

Answer 3

any series where it is (1 / a ^ p ) where a > 1 converges, but if a <= 1 it diverges.

Question 4

Remainder formula

Answer 4

integral from n + 1 to infinity <= Rn <= integral from n to infinity

Question 5

Form of (a / b)^n

Answer 5

Geometric series, if a / b < 1, converges

Question 6

Form of 1 / n ^ p

Answer 6

P test, if n > 1 it converges

Question 7

Harmonic series

Answer 7

1 / n does not converge

Question 8

What is an improper integral Type 1?

Answer 8

Integral to infinity

Question 9

What is an improper integral of Type 2?

Answer 9

Integral with a discontinuity

Question 10

What is the arc length formula for f(x)?

Answer 10

sqrt(1+f’(x)^2) (plug this into an integral)

Question 11

What is the formula for surface of revolution

Answer 11

2piradius*sqrt(1+f’(x)^2)

Question 12

Formula for hydrostatic pressure

Answer 12

P = pgd

Question 13

Formula for trapezoidal rule

Answer 13

(b-a)/(2n) * (f(x) + 2f(x) + f(n))

Question 14

Formula for moment of system around the y axis (M sub y)

Answer 14

Sum(m sub i * x sub i)

Question 15

Formula for moment of system around the x axis (M sub x)

Answer 15

Sum(m sub i * y sub i)

Question 16

Formula for center of mass given M sub y and M sub x

Answer 16

(M sub y / sum(m sub i), M sub x / sum(m sub i))