Calc I Test 3 Hsc

Front 1

How to find H.A

Back 1

divide all terms by the highest term in the denominator

Front 2

when finding HA, if the numerator is less than the degree of the denominator

Back 2

the limit as x approaches pos/neg infinity is zero

Front 3

when finding HA if the degree of the numerator is higher than the degree of the denominator

Back 3

then the limit as x approaches pos/neg infinity is infinity (either pos or neg depending on the sign)

Front 4

when finding HA, if the degree of the numerator and denominator are equal

Back 4

then the limit is the ration of the leading coefficients.

Front 5

name the 7 steps to curve sketching

Back 5

1. Find the domain - which will indicate if it is continuous.
2. Find all intercepts
3. Find all asymptotes
4. Find critical numbers and determine increasing or decreasing
5. Find coordinates of relative extrema
6. find inflection points and concavity.
7. Sketch and plot

Front 6

how to find y intercept

Back 6

set y to zero and solve

Front 7

how to find x intercept(s)

Back 7

set x (s) to zero and solve

Front 8

how to find vertical asymptotes

Back 8

these are the same as the zeros in the domain.

Front 9

how to find critical number

Back 9

take first derivative
-set equal to zero - by sure to include zeros from domain.
-determine increasing and decreasing by making a number line and plotting points (plug into the first derivative)

Front 10

find coordinates of extrema

Back 10

plug extrema into original equation

Front 11

slant asymptote

Back 11

the graph of a rational function, having no common factors and whose denominators are degree 1 or greater, has a slant asymptote if the degree of the numerator exceeds the degree of the denominator by exactly 1.

Front 12

how to determine inflection points and concavity

Back 12

find second derivative.
set equal to zero and find zeros
sketch a number line and test values in second derivative for pos/neg where pos=concave up and neg=concave down.

Front 13

tangent line approximation formula

Back 13

y=f(c)+f'(c)(x-c)

Front 14

formula for actual change in y and approx change in y

Back 14

actual: deltay=f(c+deltax)-f(c)
estimate: deltay=f'(x)dx

Front 15

propagated error

Back 15

the difference between exact value and measured value
f(x+ deltax ) - f(x) = deltay

deltaX = error in measurement
deltay= propagated error

Front 16

draw first quadrant of units circle

Back 16

draw first quad of unit circle

Front 17

formula for using differential to approximate the value of a function

Back 17

f(x + delta x) is approx = to
****f(x)+f'(x)dx

Front 18

newtons method

Back 18

start with an x1 as a guess close to the c (as to do fewer interactions)
x1 - [ f(x1)/f'(x1) ]= x2 , where x2 is interaction 2. Then sub in all x2 to find interaction x3.

Front 19

derivative of : cosx

Back 19

-sinx

Front 20

derivative of : sin

Back 20

cos

Front 21

derivative of :tan

Back 21

sec^2

Front 22

derivative of : secx

Back 22

secx tanx

Front 23

derivative of : cotx

Back 23

-csc^2x

Front 24

derivative of : csc x

Back 24

-cscx cotx