Math 175 Test 3 Review

L'Hôpital's Rule (6.8)

100

L'Hopitals rule is used for these types of limits

What are indeterminate forms 0/0 and ∞/∞?

200

Note Card 200

0

300

The justification required when moving the limit inside the function e^u or ln(u)

(example: lim(x->2) e^x+1 = e^{lim(x->2)(x+1)})

What is "By continuity (of e^x)"

400

Note Card 400

1

500

Note Card 500

e³

Integration By Parts (7.1)

100

The formula used to do integration by parts

What is uv - ∫v du ?

200

The order of priority for choosing 'u' in an integral by parts

What is:
    Logarithmic functions
    Inverse trigonometric functions
    Algebraic functions
    Trigonometric functions
    Exponential functions?

300

∫te^2tdt

What is 1/2*te^2t -1/4*e^2t + C

400

∫e^3xcosx dx

What is 1/10*e^3xsinx + 3/10*e^3xcosx + C

500

∫ln(x)dx

What is x*ln(x) - x + C

Trigonometric Integrals (7.2)

100

∫sin(x)dx

What is -cos(x) + C

200

These are the three Pythagorean identities

What are: 

sin²θ + cos²θ = 1,

1 + cot²θ = csc²θ,

and tan²θ + 1 = sec²θ?

300

∫tan²x dx

tanx - x + C

400

Note Card 400

1/2*sin(2x) + C

500

∫sin²x sin2x dx

1/2*sin⁴x + C

Trig Substitution (7.3)

100

The justification required when doing the initial trigonometric substitution

What is θ = arc[trig](x) OR lower bound ≤ θ ≤ upper bound?

200

cosθ in terms of x given θ = arcsin(3/x)

What is √(x²-9)/x?

300

The bounds of the below integral after the trig substitution

What are π/4 and π/6?

400

The integrand of ∫√(x²+4)dx in terms of θ

What is 4sec³θ?

500

dx in terms of θ if θ = arctan(10x/3)

What is 3/10*sec²θ dθ

Justin's Hot Takes

100

The single best subject no diff

What is math?

200

This is a common inquiry about the genre of music which is objectively the best (and it's not even close)

"Ya like jazz?"

300

The single worst condiment, though it is a close call

What is ketchup?

400

The calendar date of "the day before the night before Christmas"

What is December 24th?

500

The colors of Math, Science, History, and English (as in what color folder or notebook one would use for that subject)

Green, Blue, Yellow, and Red respectively