Calc 1

Instantaneous rate of change

slope

M=f(b)-f(b)/b-b

F(6)=4

Lim f(x)=3

X→6-

lim f(x)=3

X→6+

Overall:

Lim f(x)=3

X→6

f(4)=5

Lim f(x)=2

X→4-

Limf(x)=5

X→4+

Overall:

Lim f(x) DNE

X→4

(Don’t put equal sign)

DNE vs Undefined

limits: DNE Limf(x) DNE

Functions: undefined F(2) is undefined

(Holes are undefined)

Difference quotient

subtract, divide

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

Properties of limits

Find Limit of rational function

1. Direct substitution

2. #/0 vertical asymptote at the number plugged in. Determine if it’s possible infinity or neg

3. 0/0 - indeterminate form, factor, rationalize, or apply trig identities

(When writing- don’t stop writing Lim x→# until you plug the number in at end)

Squeeze theorem

Lim sin x / x

X→0

1

Lim x / sin x

X→0

1

Lim 1-cos x / x

X→0

0

Pythagorean identities

Cos²x+sin²x=1

Cos²x=1-sin²x

Sin²x=1-cos²x

Sec²x=1+tan²x

Csc²x=cot²x+1