implicit differentiation Find tangent of expression with both xs and ys: Steps: 1. ___________________ 2. find dy/dx -> plug in points to get slope If ________________ and _________________ have the same sign at any specific point, speed is increasing. Integrating the "u" means adding ______ to u's exponent, ____________ the exponent, and putting it in front finding the vertical tangent: __________________________________

Find tangent of expression with both xs and ys: Steps: 1. ___________________ 2. find dy/dx -> plug in points to get slope

special, directly, limits, tactics, REAL, equal integral of 1 find the min/max position/velocity means Find k to make f(x) continuous: Steps: 1. plug in the "________" value __________ into the __________ for both, likely yield 0 2. when they do, use "special _________" to get the __________ limit for each 3. set the two limits ___________ to each other In a water level changing problem, leakage (volume) means a

Find k to make f(x) continuous: Steps: 1. plug in the "________" value __________ into the __________ for both, likely yield 0 2. when they do, use "special _________" to get the __________ limit for each 3. set the two limits ___________ to each other

f'', through, number line, pos, neg, signs, POI, f Find the coordinates of POI and justify: Steps: 1. get ____(x) 2. find zeroes (doesn't have to go _______) 3. plot zeroes on a ___________ _______ and ______/_______ the line 4. ones that change ___________ are ___________ 5. plug "good ones" into _______(x) When finding the derivative of an integral, should + c be included? Ex. Find the integral of -2 to 5 OF 2f(x)+3 Steps: -2 to 5 f(x) dx + -2 to 5 3 dx 2(-3) -> b/c 2 times f(x) + 3(-2) - 3(5) -> b/c integral of 3 is ______ = -27 (9/8/20) Find the average velocity means do the ________________________ formula.

Find the coordinates of POI and justify: Steps: 1. get ____(x) 2. find zeroes (doesn't have to go _______) 3. plot zeroes on a ___________ _______ and ______/_______ the line 4. ones that change ___________ are ___________ 5. plug "good ones" into _______(x)

area, adds up all the signs to the total amount of fence, exploit secondary, other side, primary, derivative, 0s integral of 1 In a trapezoid, the bases are _________________. The height is _______________. the derivative of sin(x+2) is Find the maximum/minimum area of fenced in area: Steps: 1. set up "primary" equation that could find the __________ of the shape 2. set up "secondary" equation that ___________________________ 3. "__________" ______________ to get a single variable 4. plug in the "_______ _________" of the single variable into the "queen" AKA ___________ 5. find _____________ of primary, number line and neg/pos the _______ of the der. 6. change from neg to pos means min, pos to neg means max 7. the special number line value is the x/y from the "other side" of step 4

Find the maximum/minimum area of fenced in area: Steps: 1. set up "primary" equation that could find the __________ of the shape 2. set up "secondary" equation that ___________________________ 3. "__________" ______________ to get a single variable 4. plug in the "_______ _________" of the single variable into the "queen" AKA ___________ 5. find _____________ of primary, number line and neg/pos the _______ of the der. 6. change from neg to pos means min, pos to neg means max 7. the special number line value is the x/y from the "other side" of step 4

1, reversing/swapping Rectangular Prism Volume Find absolute extrema: Steps: 1. find the _____________ of the __________________ 2. plug in these numbers and the ___________ endpoints into the ___________ Integrating the "u" means adding ______ to u's exponent, ____________ the exponent, and putting it in front point of inflection

Integrating the "u" means adding ______ to u's exponent, ____________ the exponent, and putting it in front

right, top, higher, lower, ADD In area bounded by problems (w/ integrals), round to __________ decimal places. Find the exact area bounded by f(x) and g(x): Steps: 1. you can write down the points, but it might be easier to visualize 2. ___________ x goes on ____________ of the integral, left x goes on bottom 3. _________ minus _________ for inside the integral 4. do for both "circles" if necessary - if so, _____________ them finding the vertical tangent: __________________________________ the derivative of 2f(x) is __________________

Find the exact area bounded by f(x) and g(x): Steps: 1. you can write down the points, but it might be easier to visualize 2. ___________ x goes on ____________ of the integral, left x goes on bottom 3. _________ minus _________ for inside the integral 4. do for both "circles" if necessary - if so, _____________ them

negative number Find all times the object moves right and left: Steps: 1. find ____________ of ____________ 2. ____________ line 3. right is positive (like physics) If you are doing U-Substitution and there is a squared trig function and a normal one, pick the ___________ one to be the "u." Domain Rules: 1. for fractions -> set __________ = ___________ and exclude those values 2. radical -> _____________ than or equal to 0, solve IF MULTIPLE VALUES DO _______________ ______________ -> ___________ result means range WORKS 4. absolute value -> set inside equal to _________, NUMBER LINE -> negative means "meat" is ____________ for that range, positive means "meat" is positive for that range -> make _______________ In a water level changing problem, leakage (volume) means a

In a water level changing problem, leakage (volume) means a

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Calculus - Geometry

snashuhaimdinx Created by 6 mon ago

Cards in this deck(61)

implicit differentiation

special, directly, limits, tactics, REAL, equal

f'', through, number line, pos, neg, signs, POI, f

derivative is 0 or DNE

area, adds up all the signs to the total amount of fence, exploit secondary, other side, primary, derivative, 0s

1, reversing/swapping

right, top, higher, lower, ADD

negative number

cos(x+2)

Add 1 to the power and divide by the new power

+ c

V=lwh

V=πr²h

V=1/3π(r^2)h

4/3πr³

only the cos/sin itself!

u = sin(5x)

squared *make sure it is in singular form, though!*

d/dx ∫ f(n) dn = f(x)

just plug in the x

NEGATE

multiply by the derivative of the expression

negate and multiply by the derivative

top and bottom are #s "burger" still has the X (think burger means death -> X) d/dx

When finding the derivative of an integral, DO NOT include +c !!

inside, outside

A=1/2h(b1+b2)

what's on the x-axis

bottom, 0, greater, number line, positive, inside, negative, PIECEWISE

y, f(x) = f(-x)

-f(x) = f(-x)

the limits at infinity and negative infinity

denominator, 0, x, limits, VA, hole

inside

f(x) at different x-values, the difference in the x-values themselves

ignore, trick (the trick is plugging in 1000 and -1000 via limits, respectively)

VA, hole

2f'(x)

because f(2) is increasing throughout, f'(2) is + throughout, and f''(x) is concave up. (9/11/23 -> check!)

concave up, exponential

X, V, A

velocity, position, bottom up

average value

roots, velocity, number

velocity, acceleration

the x-axis

interval, original

point where concavity changes AKA f''(x) changes signs

roots, original

f'(x)

integrate the x first before doing anything! make sure you actually integrate

negative

find the roots of the derivative and evaluate

.5bhl

turn

it loses the equals in < and >

find where the derivative is undefined

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