Yellow Card Stuff to Know

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48 Terms

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sin(u)

cos(u)

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cos(u)

-sin(u)

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tan(u)

sec2(u)

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cot(u)

-csc2(u)

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sec(u)

sec(u)tan(u)

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csc(u)

-csc(u)cot(u)

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ln(u)

1/u

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eu

eu

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sin-1(u)

<p></p>
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cos-1(u)

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tan-1(u)

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cot-1(u)

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Limit from the left of f(x) as x → a

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Limit from the right of f(x) as x → a

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Definition of Continuity

  1. f(a) is defined

  2. Limit from left = limit from right

  3. Overall limit = f(a)

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Chain rule

f’(u) * u’

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Product Rule

uv’ + u’v

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Quotient Rule

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Intermediate Value Theorem

If f is continuous on the closed interval [a,b], where f(a) ≠ f(b) and k is a number between f(a) and f(b), then there is atleast one number c in (a, b) such that f(c) = k.

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Mean Value Theorem

If f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c such that:

<p>If <em>f</em> is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c such that: </p>
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L’Hopital’s Rule

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Critical Points

If f(x) is defined at x = c, then f(x) has a critical point at x = c if f’(c) = 0 OR f’(c) is undefined.

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Global Minimum

f(c) < all other values of f(x)

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Global Maximum

f(c) > all other values of f(x)

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Extreme Value Theorem

If f is continuous on the closed interval [a, b], then f has both an absolute minimum value and absolute maximum in the interval.

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F + G

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F - G

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FG

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Fn

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F/G

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1

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0

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Fundamental Theorem of Calculus

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<p>Corollary to FTC</p>

Corollary to FTC

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If continuous on [a, b] and x=c on (a, b) then…

(MVT/average value for integrals)

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Disk Method

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Washer Method

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General volume equation

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Arc Length (rectangular)

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velocity

s’(t)

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acceleration

s’’(t) = v’(t)

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Speed (parametric and rectangular)

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Displacement

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Average velocity

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Euler’s Method

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Integration By Parts

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<p>Logistics</p>

Logistics

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