midterm 3 true/false

false → anything that is infinity^infinity will just go to infinity

true → 1/0 will go to infinity and cos(0) = 1 so it will be 1^infinity

false → this is the definition of e^x; therefore, it would result in e²

false → l’hopital’s rule finds the derivative of each the numerator and denominator, you do NOT use the quotient rule to find it

true → definition

false → you have to split it where it does -1 to 0 + 0 to 1

• if one side diverges, they both diverge

saying that an improper integral converges means that the integral must evaluate to a finite number

true → converges = finite number

indefinite integrals can be improper

false → must evaluate to either infinity or a finite number

If {An} is bounded, then it converges

false → sequence must be BOTH monotonic and bounded to converge

if {An} converges, then it is monotonic

false → sequence must be BOTH monotonic and bounded to converge

An unbounded sequence diverges

true → unbounded = diverge

false → it can also oscillate

true → long term limit

false → harmonic series

• the series always diverges

true → definition

true → harmonic series

the sum of two divergent series also diverges

true

false → geometric series

• the majority of this statement is correct BUT n must equal 0 for the statement to be 100% correct

integral test & nth term test

1. statement regarding test you are using and any/all conditions

2. math step

3. conclusion statement

Integral Test

1. positive

2. decreasing

3. continuous