Calculus Rules Sheet Game!

Question 1

L'Hopital's Rule can be used for each of these below except...

Accepted Answer

1/0

Question 2

∫secxtanx dx =

Accepted Answer

secx + C

Question 3

Find lim (4x2/3x) as x goes to infinity!

Accepted Answer

∞

Question 4

If f''(x) > 0, then by the 2nd Derivative Test, x is...

Accepted Answer

a relative min

Question 5

What is like the Chain Rule for integrals (what some call the "Anti-Chain-Rule")

Accepted Answer

U-subs

Question 6

Handling Riemann sums with equal intervals, you first get endpoints using what formula?

Accepted Answer

Δx = (b - a)/n

Question 7

Find the domain of y = ln√x

Accepted Answer

(0, ∞)

Question 8

What's the derivative of log2x?

Accepted Answer

1/(xln2)

Question 9

∫-cosx dx =

Accepted Answer

-sinx + C

Question 10

You switch x and y to find what of a function?

Accepted Answer

inverse

Question 11

∫e2x dx =

Accepted Answer

e2x/2 + C

Question 12

If the units on x and y will cancel when you multiply them, what should you do?

Accepted Answer

integrate

Question 13

∫4x dx =

Accepted Answer

4x/ln4 + C

Question 14

What's the HA of y = ex?

Accepted Answer

y = 0

Question 15

What do we call something with a critical point that's not a relative max or min?

Accepted Answer

saddle point

Question 16

Trap Rule says area is approx (b - a)/2n (f(x0 + ? + ? + ...f(xn). What are ?'s

Accepted Answer

2f(x1) and 2f(x2)

Question 17

#/-∞ or #/∞ =

Accepted Answer

0 for both

Question 18

What formula do you use to find the period of a sinusoid?

Accepted Answer

kP = 2π

Question 19

You put in -y for y to see if a function has what kind of symmetry?

Accepted Answer

x-axis

Question 20

The Mean-Value Th'm for derivatives says f'(c) = (f(b) - f(a))/(b - a) if diff & cont. So ? and ? are ?. ?'s(in order)

Accepted Answer

tangent, secant, parallel

Question 21

Find all horizontal tangents of y = cosx on [0, 2π)

Accepted Answer

at x = 0 and π

Question 22

On a 30°/60°/90° triangle, what side is across from 60°?

Accepted Answer

√3

Question 23

Name a "cheesy" statement your teacher said at the beginning of the year to thank you all for taking this class...

Accepted Answer

Thanks for putting the 'us' in 'Calculus'!

Question 24

For absolute extrema, you check f(what 2 types of points)?

Accepted Answer

critical and end

Question 25

Suppose they give you a graph of f'. To find where f is increasing, you'd...

Accepted Answer

look where the graph is above the x-axis

Question 26

Since v(t) = t + 1 is linear, you can also find the average velocity from 0 to 2 by going...

Accepted Answer

(v(2) + v(0))/2

Question 27

Give an example of something with a critical point that's a point of non-diff.

Accepted Answer

vertex of absolute value graph

Question 28

If they ask you to justify relative extrema or inflection points, they want you to do what?

Accepted Answer

make number lines

Question 29

Getting an LCM, factoring, foiling, & rationalizing are all things you do if you get what?

Accepted Answer

0/0

Question 30

∫1/x dx =

Accepted Answer

ln|x| + C

Question 31

The Shell method for finding volume has 2π∫h(x) ? dx. What's ?

Accepted Answer

p(x)

Question 32

When finding area between curves, how can you tell if wrtx or wrty?

Accepted Answer

vertical = x; horizontal = y

Question 33

sin2x + ? = 1

Accepted Answer

cos2x

Question 34

How would you find the average acceleration from 0 to 2 sec if v(t) = t + 1 still?

Accepted Answer

(v(2) - v(0))/2

Question 35

1 + tan2x =

Accepted Answer

sec2x

Question 36

∫secxtanx dx =

Accepted Answer

secx + C

Question 37

Find the only thing not true about y = lnx.

Accepted Answer

It goes through (0, 1)

Question 38

∫1/(2x - 1) dx =

Accepted Answer

(1/2)ln|2x - 1| + C

Question 39

If you're handling a related rate problem, you should derive with respect to what?

Accepted Answer

t

Question 40

∫x3dx =

Accepted Answer

x4/4 + C

Question 41

What type of Riemann sum adds inscribed rectangles?

Accepted Answer

Lower Sum (SL)

Question 42

You are given a v(t) equation. How would you find displacement?

Accepted Answer

integrate

Question 43

Drawing random tangent slopes at points on an x,y plane is called...

Accepted Answer

a slope field

Question 44

What points have f''(x) = 0 or ∅ and change signs around them on a number line?

Accepted Answer

inflection points

Question 45

Rolle's Th'm is just like the MVT for derivatives, only the slopes (tangent & secant) are...

Accepted Answer

0

Question 46

What's the derivative of 32x?

Accepted Answer

2(32x)ln3

Question 47

If v(t) = t + 1, on [0, 2], name how you should find the average velocity.

Accepted Answer

the integral of t + 1 from 0 to 2 all divided by 2

Question 48

What's the derivative of cotx?

Accepted Answer

-csc2x

Question 49

odd functions have symmetry around...

Accepted Answer

origin (x & y axes)

Question 50

For the disc & washer methods, rectangles are drawn ___________ to the axis of revolution.

Accepted Answer

perpendicular

Question 51

Which Riemann Sum uses area being approximately Δx⋅f(average endpts)?

Accepted Answer

Midpoint Sum

Question 52

They give you a v(t) equation of a spider. How do you find where the spider went to the right?

Accepted Answer

it's where its velocity is positive

Question 53

the MVT for integrals says if a function is continuous, then the area under the curve from a to b for f(x) dx = ?(b - a)

Accepted Answer

f(c)

Question 54

Suppose you're doing the Shell method but have h(y). Then it's important to remember that h(y) is...

Accepted Answer

right - left

Question 55

Limits toward infinities (positive or negative)...unless they come out -∞ or ∞, give us what?

Accepted Answer

HA's

Question 56

Suppose you're given a graph of f' again. If they ask you to find where inflection points of f are, you should...

Accepted Answer

look where you can draw tangents on f' that are 0 or undefined

Question 57

Where does y = x2 - 2x have a horizontal tangent?

Accepted Answer

at x = 1

Question 58

logar =

Accepted Answer

rloga

Question 59

A function is concave down when...

Accepted Answer

f''(x) < 0

Question 60

What's the derivative of ln(.5x)?

Accepted Answer

1/x

Calculus Rules Sheet Game!

Questions 60

Calculus Rules Sheet Game!

Questions 60