AP Calculus AB Quarter 1 Exam

Tangent Line

Y=f′(a)(x+a)+f(a)

It’s the line that touches a curve at a single point, representing the instantaneous rate of change of the function at that point.

Infinite Discontinuity

Vertical Asymptotes (Set = to Zero)

sets of points that can be approached but never actually reached.

Removable Discontinuity

Hole (Cancels out)

Where there is a hole in the graph of a function where a limit exists, but the function is not defined at that point.

Jump Discontinuity

Quotient Rule

f′(x)g(x)-f(x)g′(x)/g(x)²

Product Rule

f′(x)g(x)+f(x)g′(x)

y=e^x

e^x

y=Sinx

cosx

y=cosx

-sinx

y=a^x

lna×a^x

y=lnx

1/x

y=√x

1/2√x

y=tanx

sec²x

y=cotx

-csc²x

y=secx

secx×tanx

y=cscx

-csc×cotx

Continuity

Left Limit= Right Limit=f(a)

Differentablity

Left Derivative= Right Derivative

x³/x^5

y=0

Nikki Minaj (Small on top- Big on bottom)

x^5/x

Equals DNE

Dolly Parton (Big on top- Small on bottom)

x^4/x^4

Divide them

y=Coefficient/ Coefficient

Average Rate Of Change

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

Intermediate Value Theorem

1.Prove Continuous

2.Plug In Endpoints

3.Verify Value Your Testing Is Between Endpoints

4.Write Sentence USING IVT