Calculus - Beginning Limits

Ms. Parker trivia

100

How many kids does Ms. Parker have?

3

200

Name at least one college from which Ms. Parker received degrees.

Elmira College, Marist College

300

Name at least one sport Ms. Parker still participates in as an adult.

volleyball, crew

General Limits Info

100

Name three times when a limit does not exist.

1. f(x) approaches a different number from left and right side of c 2. f(x) increases or decreases without bound 3. f(x) oscillates between two fixed values

200

What does the notation lim x->8 f(x) = 25 mean?

As x approaches (gets very close to) 8, f(x) approaches 25

300

If f(2)=4, can you conclude anything about the limit of f(x) as x approaches 2?

No

400

If the limit of f(x) as x approaches 2 is 4, can you conclude anything about f(2)?

No

500

True/False: If f(a) is undefined, then the limit as x approaches a will also be undefined.

False

600

State the 3 rules for limits to infinity.

Top heavy: +/- infinity

Bottom heavy: 0

Powers equal: divide coefficients

700

When is the function f(x) continuous at x=c (by calculus standards)?

f(c) is defined,

lim_(x->c) f(x)

 exists , 

lim_(x->c)f(x)=f(c) 

Limits

100

lim_(x→2) ⁡3/(4x)

3/8

200

lim_(x→-3)⁡ (x^2+x-6)/(x^2-9)

5/6

300

lim _(x→-1)⁡ (x2-1)/(x+1)

-2

400

lim_(x→0) ⁡cos⁡x

1

500

lim_(x→4)⁡(x^2-5x+4)/(x^2-2x-8)

1/2

600

lim_(x→−3) (x^2-x-12)/(x+3)

-7

700

lim_(x→3)⁡(√(x+1)-2)/(x-3)

1/4

Miscellaneous

100

Determine if any discontinuity(ies) exists for

f(x)=(x-1)/(2x^2-2)

non removeable discontinuity (vertical asymptote) at x =-1

removeable discontinuity (hole) at x=1

200

Determine if any discontinuity(ies) exists for

f(x)=(x^2+2x-8)/(x^2-4)

non removeable discontinuity (vertical asymptote) at x =-2

removeable discontinuity (hole) at x=2