Class notes

Class notes Calculus I

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Course
Calculus I

Institution
(At Home Study)

38 Pages of Notes taken in my spare time following Professor Leonard’s calculus 1 course on YouTube. Formally defining the Fundamental Theorem of Calculus. Beginning with an introduction to Limits, followed by definition of a derivative. Continues with Chain Rule, Product Rule, Quotient Rule, Pow...

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Uploaded on December 28, 2023
Number of pages 38
Written in 2022/2023
Type Class notes
Professor(s) Professor leonard
Contains All classes

math
mathematics
calculus
calc1
calc
derivative
integral
integration
limit
limits
differentiation
u substitution
chain rule
power rule
antiderivative
product rule
quotient r
definition of a derivative

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4 items

1. Class notes - Class notes calculus i
2. Class notes - Class notes calculus ii
3. Other - Identities sheet
4. Class notes - Class notes calculus iii
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CalculusI -
Intro to Limits

Goals of Calculus Ex : f(x) = x2

(x xy) slope

thearea
· (x y) m =

# findi S
T +
point
,
,
of ,
>
-
function
a
& As Q + P

P(1 1)
Mse
· >
Mean
-
,

Eg for tan : & X & I -> undefined

mcn(Xc )
> Site Y y = - X
, Q + P
points two
between
(
Man =
X -
I

X
I -
1

Tangent Problem
↳ becaus X already cannot and will not equl 1.

#decant
- X+ )
ms =

live What ?
happens to
msen as X-1
↳ More
Q mely close to P (but not 4) ↳
Msec-> 2
the secant live becomes (essentially) a

tangent line Because More-> 2
(slope of sea live approaches 2)
...
BUT ↳
Mean = 2 (slope of tan lime actually is .
2)
5For a line , you
need two points (P + Q) 1 = 2(x D -

y
-

↳ As Q approaches P ,
the secant
gets closer to the
y -
1 = 2x -
2

F2x- 11
>

tampant of P
Ein - >

& If Q -P but Q & P
,
the secant will be identical
t the tangent A limit must approach the same value from
↳ THIS A
IS "LIMIT" either side.

I General
limf(x) = L

*I
Spill in 4973 4 .

Sided Limit
Right
↳im f(x) ,
->

/im f(x) ,

↳im f(x) =
(imf(x)

No
For a limit to exist at a

↳ limf(x) =
limf(x)
ab
X> -
2 x -

, 2

Computing Limits
Lim (x-2x
Basics Lim
: c = c (constant

[imx] (in2) (in ** ·

Sim
Lim x
-a

23 -
2 .

207

*
Els ↓im (x2xx) =
= o
-

-

D

Xin = D

fla
↳im f(x)
=

Properties :
Lim f(x) =L
lim X- 4

#(x
2x2
(X -
2
2
2)
+

Xim g(x) L This isskay
x + 2 -

X
=

because crib

i
we

X bo = 2

1
m [f(x) g(x)] = imf(x) my
+
allowing
anyway

2 .
xina(f(x) g(x)] Ximf(x) /lim g(x)
· = ·
-

Lim

3
.
lim( x , Lim g(x lim
x+
3
x2 - 3x-10
x 25 -
- Limitdis

4 .

/ima [f(x)]" =

[limf(x)]" Note
↳ If 8 factor simplify
↳ Lim
and

= f(x) ↳ If you
,

can't simplify the Sinlysis
& I It

:
problem away
. .. It isn't a -
2

hole .

Evaluate
min
↳ sign analysis
>
-

N
Xim 1 1 2
= + =
+

lim M I ·
/
=
16X -

-

X- y X

lim
+ o ) = i

,
,

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