Day 1 & 2
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
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,
you can use ___________ _____________ so long as the denominator of the rational function evaluated at c is not 0.
Direct substitution
f(a)=b/0
what is most likely the probably case?
Asymptote probably.
The instantaneous rate of change is abbreviated as ...
(I.R. of C)
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)
What is the notations of the limit of the identity function?
lim_(x->c) x=c
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
f(a) = b where b is a
R
means what is most likely found?
limit found probably
I.R. of C formula is written as ?
m= lim_(h->0) (f(x+h)-f(x))/ h
What is the equation for the left hand limits?
lim_(x->c^-) f(x)=L_1
Which Property is this applies to the following function:
lim_(x->c) kf(x)= k lim_(x->c)f(x)
scalar Multiple Property
Find
lim_(x->1) f(x) (x^2 -1)/(x-1)
=2
f(a)= 0/0
what form are we dealing with?
Indeterminate form
Find an equation for the slope of a function at any point.
y=x^2 +3
2X
What is the equation for the right hand limits?
lim_(x->c+) f(x)=L_2
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.
lim_(x->9) (sqrtx -3 )/ (x-9)
1/6
What are other methods we learned about that come from a
f(a) =0/0
factoring
conjugates
Factor
(x+1)(x+1)(x+1)
(x^2+2x+1)(x+1)= x^3 +2x^2+x+x^2+2x+1
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.
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
lim_(x->4)(sqrtx-2)/(x-4)
1/4
lim_(x->-1) (x^2-x-2)/(x^2-2x-3)
=3/4
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