I missed my first day of calculus so can someone help me understand what they went over. It's limits, one sided limits, computing limits, and piecewise defined functions
I missed my first day of calculus so can someone help me understand what they went over. It's limits, one sided limits, computing limits, and piecewise defined functions
I missed my first day of calculus so can someone help me understand what they went over. It's limits, one sided limits, computing limits, and piecewise defined functions
I missed my first day of calculus so can someone help me understand what they went over. It's limits, one sided limits, computing limits, and piecewise defined functions
Transcribed Image Text:TFW
10:20 AM
O 80%
ues for Computing Limits
2 of 2
fined when X= q and for all x near a, then the
limit may be computed by direct substitution
lim
lim
e.g. x2 [5x*+1]
: 5(2)*+ 1
Poly nomial functions: xa f(x) - f(a)
=21
lim, P(X)
lim pex)
Rational functions: x+a q(x)
lim
if yla) *0
lim
e g. *+2 [sx'+1]
: 5(2)* +|
= 21
Piecewise - Defined Functions
lim
Find f(x) - if x2
X+3 if x>2
lim
*+2- f(x) = : 3
lim
x+2* f(x) : 2+3 : 5
lim
So, xa f(x) does not exist
O attachments.office.net
Transcribed Image Text:TEW
10:20 AM
O 80%
## 2.2 and 2.3 a, Limits ##
Informal Definition of a Limit x. f (x) -L, “limit as
X approaches a of f(x) equals L" if f(x) gets closer to L
as x gets closer to
lim
a from both
lim
* f(X) : 3
X +4
f(x) = 2
e.g.
One - Sided Limits.
Right -hand Limit: xa* f(x) = L ,
if f(x) gets closer to L as x gets closer to a for x 7 a.
K limit as x •pproaches a from the
right equals L",
Tim
Left -hand Limit: f (x): L,
if f(x) gets closer to L as x gets closer to a for x <a
4 limit as x approaches a frum the
left equals L",
e.g *
*40* fx) = |
lim
X+0" f(x) does not exist
lim
Theorem: If a flx) = L and **a-f(x) = L, then a f(x) = L
0therwise, xa f(x) does not exist
lim
Tim
X+-+ f(x) = 0
X- f(X) : 3
Tim
X+3 f(x) • o
e.g.
lim
x41 f(x) does not exist
2.3 a Iechniques for Computing Limits
If f(x) is defined when x:9 and for all x near a, then the
limit may
be computed by direct substitution
lim
lim
e.g. X+2 [5x*+1]
: 5(2)*+ 1
: 21
Poly nomial functions: x*a f(x) = f(a)
lim Plx)
lim
attachments.office.net
Definition Definition Group of one or more functions defined at different and non-overlapping domains. The rule of a piecewise function is different for different pieces or portions of the domain.
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![TFW
10:20 AM
O 80%
ues for Computing Limits
2 of 2
fined when X= q and for all x near a, then the
limit may be computed by direct substitution
lim
lim
e.g. x2 [5x*+1]
: 5(2)*+ 1
Poly nomial functions: xa f(x) - f(a)
=21
lim, P(X)
lim pex)
Rational functions: x+a q(x)
lim
if yla) *0
lim
e g. *+2 [sx'+1]
: 5(2)* +|
= 21
Piecewise - Defined Functions
lim
Find f(x) - if x2
X+3 if x>2
lim
*+2- f(x) = : 3
lim
x+2* f(x) : 2+3 : 5
lim
So, xa f(x) does not exist
O attachments.office.net](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f8bf5c4-2067-44fc-9f2b-c5b4c75aa339%2F3e4b9b34-6671-4418-a9f3-0626c752c493%2F35wha7_processed.png&w=3840&q=75)
![TEW
10:20 AM
O 80%
## 2.2 and 2.3 a, Limits ##
Informal Definition of a Limit x. f (x) -L, “limit as
X approaches a of f(x) equals L" if f(x) gets closer to L
as x gets closer to
lim
a from both
lim
* f(X) : 3
X +4
f(x) = 2
e.g.
One - Sided Limits.
Right -hand Limit: xa* f(x) = L ,
if f(x) gets closer to L as x gets closer to a for x 7 a.
K limit as x •pproaches a from the
right equals L",
Tim
Left -hand Limit: f (x): L,
if f(x) gets closer to L as x gets closer to a for x <a
4 limit as x approaches a frum the
left equals L",
e.g *
*40* fx) = |
lim
X+0" f(x) does not exist
lim
Theorem: If a flx) = L and **a-f(x) = L, then a f(x) = L
0therwise, xa f(x) does not exist
lim
Tim
X+-+ f(x) = 0
X- f(X) : 3
Tim
X+3 f(x) • o
e.g.
lim
x41 f(x) does not exist
2.3 a Iechniques for Computing Limits
If f(x) is defined when x:9 and for all x near a, then the
limit may
be computed by direct substitution
lim
lim
e.g. X+2 [5x*+1]
: 5(2)*+ 1
: 21
Poly nomial functions: x*a f(x) = f(a)
lim Plx)
lim
attachments.office.net](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f8bf5c4-2067-44fc-9f2b-c5b4c75aa339%2F3e4b9b34-6671-4418-a9f3-0626c752c493%2F2tzprsi_processed.png&w=3840&q=75)
