exam review

Question 1

how do you find zeroes?

Answer 1

make original equal to zero, and solve. (factor and use outside as one answer, inside as another and set those to equal to zero to find answer)

Question 2

how do you know if there aren’t asymptotes?

Answer 2

its not being divided by a variable

Question 3

how do you find local extremes?

Answer 3

take the first derivative, make it equal to zero and solve. (factor and inside is one answer, outside is another and solve when equaled to zero)

Question 4

how do you find inflection points?

Answer 4

using the second derivative and solving when equaled to zero. OR if two local extremes show up twice, they are deemed inflection points

Question 5

how do you do the first derivative test?

Answer 5

using your local extremes, create a number line

Question 6

how do you figure out if increasing or decreasing?

Answer 6

using the first derivative test, test the points between the intervals on your number line. when -ve, decreasing and vice versa. SUB VALUES INTO FIRST DERIVATIVE, DONT FORGET TO STATE YOUR INTERVALS IN THE END. (ex. 0<x)

Question 7

how do you do the second derivative test?

Answer 7

using your inflection points, create a number line

Question 8

how do you figure out if concave up or down?

Answer 8

follow increasing/decreasing steps BUT with the second derivative.

Question 9

what are critical points?

Answer 9

inflection points and local extremes

Question 10

what is revenue?

Answer 10

amount sold x price

Question 11

how do you complete an optimization question?

Answer 11

figure out the original equation from the text, find the first derivative and make it equal to zero then solve. this is your answer. check your work using second derivative. if it is -ve, it’s maximized and vice versa

Question 12

how do you find the linearization?

Answer 12

given x value is your a. f(a) is when you sub in your a value into the original equation. f ‘ (a) is when you sub in your a value into the first derivative. complete with the full new equation using the formula

Question 13

how to estimate values using linearization?

Answer 13

find linearization of equation, then sub in value given for x.

Question 14

how to know when your linearization is reasonable?

Answer 14

ex. if you found the linearization of 1, and you’re original value of a was 1.05, this is reasonable because 1 is close to 1.05. if it were -6, it wouldn’t be reasonable

Question 15

limits involving infinity : denom. has higher degree than num. it equals…?

Answer 15

0

Question 16

limits involving infinity : equal degrees in num. and denom., what do you do?

Answer 16

divide coeffs!

Question 17

limits involving infinity : num. has higher degree than denom. equals…?

Answer 17

dne

Question 18

when doing the sandwich theorem, if you’re multiplying by something with an ODD degree, you…

Answer 18

do abs value to the thing with odd degree in sandwich

Question 19

“average rate” hints at the question being…

Answer 19

secant

Question 20

what equation does secant use?

Answer 20

just remember m = , and that there will be two x values

Question 21

“instantaneous rate” is a hint that the question is…

Answer 21

tangent

Question 22

“equation/slope of tangent line” hints to what kind of question?

Answer 22

definition of the derivative/first principle

Question 23

when do you use integration by parts?

Answer 23

if one factor derives to zero

Question 24

when do you use LIATE?

Answer 24

by parts, it is how you figure out what to use for u

Question 25

equation for by parts

Answer 25

Sudv = uv-Svdu

Question 26

when do you use integration by sub?

Answer 26

if it looks like chain rule

Question 27

what will u be in integration by sub?

Answer 27

inside piece

Question 28

when do you use tabular?

Answer 28

like a by parts question, but use if u is a polynomial

Question 29

what if degree of num < degree of denom in partial fractions?

Answer 29

regular partial frac

Question 30

when do you use integration by partial fractions?

Answer 30

polynomial fractions

Question 31

what if degrees =/> degree denom in partial fractions?

Answer 31

divide

Question 32

what does the degree of x have to do with by parts?

Answer 32

degree of x = how many times you have to do by parts

Question 33

when do you use area under the curve (definite)

Answer 33

basic equation! “find the area underneath…”

Question 34

when do you use area between curves?

Answer 34

“determine area between…”, “bounded by…”

Question 35

when do you know it’s an initial value problem?

Answer 35

“find ___ if ___ =____”

Question 36

how do you know it’s a discs question?

Answer 36

there’s no gaps!

Question 37

how do you know it’s a washers question?

Answer 37

when there’s a gap between the function and the axis you’re asked to rotate around

Question 38

how do you know it’s a cylindrical shells question?

Answer 38

rotating around y, one function given, with respect to x ( rotating around y but variable is x)