Limits

Day 1 & 2

100

If f(x) approaches a unique value L as x approaches c from both sides, then of f(x) as x approaches c is L, is written as what?

lim_(x->c) f(x)=L

200

What are the steps to creating a table using your GCD when getting your table to start at 1.9 and not 1 

GCD step 1: 2nd Window 

TBL start 1.9 

TBL=0.01

Ind pnt Auto Ask 

Depend Auto Ask

GCD step 2: 2nd graph (table)

300

What is the equation for the left hand limits? 

lim_(x->c^-) f(x)=L_1 

400

What is the equation for the right hand limits?

lim_(x->c+) f(x)=L_2

500

What is the definition of a two-sided limits.

The limit of a function f(x) as x approaches c exists if and only if both one-sided limits exists are equal. 

Day 3 & 4

100

Based on the notes what is the English wording for the following equation:

lim_(x->c) k =k 

The limit of a constant function at any point c is the constant value of the function,

200

What is the notations of the limit of the identity function?

lim_(x->c) x=c

300

Which Property is this applies to the following function:

lim_(x->c) kf(x)= k lim_(x->c)f(x)

scalar Multiple Property

400

Which of the properties would be use when taking the following:  

lim_(x->4) (x^2-6x+ 3) 

Power property or product property, scalar multiple properties, sum and difference properties. 

500

What two properties are used and evaluate the function at the limit stated below: 

lim_(x->3) sqrt(8-x)

nth root property 

difference property 

limits of constant and identity functions 

sqrt 5

Day 3 & 4

100

you can use ___________ _____________ so long as the denominator of the rational function evaluated at c is not 0. 

Direct substitution 

200

Find the 

lim_(x-> -1)(-3x^4 +5x^3)

lim_(x->-1)(-3x^4+5x^3)= (-3(-1)^4+5(-1)^3)= -3+ -5=-8

300

Find 

lim_(x->1) f(x) (x^2 -1)/(x-1) 

=2 

400

lim_(x->9) (sqrtx -3 )/ (x-9)

1/6 

500

lim_(x->4)(sqrtx-2)/(x-4)

1/4

Day 5

100

f(a)=b/0 

what is most likely the probably case?

Asymptote probably. 

200

f(a) = b where b is a 

R

means what is most likely found?

limit found probably 

300

f(a)= 0/0

what form are we dealing with?

Indeterminate form

400

What are other methods we learned about that come from a 

f(a) =0/0 

factoring 

conjugates 

500

lim_(x->-1) (x^2-x-2)/(x^2-2x-3)

=3/4

Day 6, 7, 8, 9

100

The instantaneous rate  of change is abbreviated as ...  

(I.R. of C)

200

I.R. of C formula is written as ?  

m= lim_(h->0) (f(x+h)-f(x))/ h

300

Find an equation for the slope of a function at any point. 

y=x^2 +3

2X

400

Factor 

(x+1)(x+1)(x+1)

(x^2+2x+1)(x+1)= x^3 +2x^2+x+x^2+2x+1

500

What does the h represent in the slope m of the tangent line at (x,f(x)) line through to? 

H- horizontal distance between two points