AP Calculus Midterm Study Guide

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23 Terms

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limit

  • the tendency of a function

  • expected “y” value for a given “x” value

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derivative

  • the slope of the tangent line

  • the instantaneous rate of change

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tangent line

touches a curve only at one point & matches the slope of the curve of that point

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secant line

line that intersects the curve at 2 points

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average rate of change formula

= f(b)-f(a) / b-a

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instantaneous velocity formula

s’(t) = v(t)

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average acceleration

v(t2) - v(t1 ) / t2 - t1

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instantaneous acceleration

s’’(t) = v’(t) = a(t)

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power rule

y’ = n * x^n-1

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product rule

y’ = f(x)g’(x) + f’(x)g(x)

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quotient rule

g(x)f’(x) - f(x)g’(x) / [g(x)]²

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chain rule

y’ = f’(g(x))g’(x)

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y = sinx

cosx

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y = cosx

-sinx

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y = tanx

sec^2x

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y = cscx

-cscxcotx

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y = sec x

secxtanx

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y = cotx

-csc^2x

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explicit equation

y = x²+5 (variable by itself)

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implicit equation

x² + y² = 25 (two different variables)

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1/sin

csc

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1/cos

sec

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1/tan

cot