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Class notes

Class notes Calculus II

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46 pages
2022/2023 Written for academic year
Institution (At Home Study)
Course Calculus II
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48 Pages of Notes taken in my free time following Professor Leonard’s Calculus 2 course on YouTube. Beginning with Differentiation/Integration of Exponential Functions, followed by advanced techniques of integration such as Integration by Parts, Trig. Substitution, Partial Fraction decomposition. Continues to Improper Integrals, into Sequences and Series. Expands on Taylor/MacLauren Series, as well as various tests of convergence (Integral Test, Ratio Test, etc.). Additionally, opens discussion over parametric equations and polar coordinates.

Content preview

NaturalLogA function
↳

↳
(n1
(n Xy
=




=
0

(nx +
/ny
jxx =
I
* +


(x - x =
( )
↳ (n Y = (nx -

1y ( z) (5 1) 5
- -
- =




↳ In xr = r .
Inx

&* dx Because * is continuous ,
we must
be able it
&
to integrate
In In 3x" Ind (n30 in xi) (1220in +
2))
- =




It d
-
-




In 304/nx- 1n2- 2 Iny It turns ...
out (nx =




In * >
-


In (x* +1) -
lux" - (n(x 1) -

E1nx * (lux] =

y (j+ at) = *


Inix)
-2)((kdx
+
(nxsini(ix) - (n(x" -2) =
mn(x)0
In x50 In sin (ix) Gln(x +




k
-




5 In x > 2 In sin(ix) -

isIn(x" -2)
:

[Inx](((x)) =
*

& [5(n x = (n(x *
1) - 4(n(x -



2)]
/luxoInl - In (x-2)"] (f(q(x)) f'(q(x)) = -

q(x)

"In In
T




* ((xix1))) = 3(x x)) ·
2x = 6x(x -1) *




Grupk f(x) = In x
x((n(g(x))) 4x) =
-

q(x) =
q(x) = ex

1




Y
39((n(3xx -


1) 134 = -
6x =
2
'

*x(ix] Ex (((nx)b) -((nx) *. k
C


·
= =




]
=




V
= * =
nux)

* [In(2x)] (2xx(x) 1) ) -




202(X 1)*. 3x -




54fxdx = za &
zi) 25
3x2




(4xsdx = 4 .
-

Ssinx dx = -cosXbc

,
,
,

Document information

Uploaded on
December 28, 2023
Number of pages
46
Written in
2022/2023
Type
Class notes
Professor(s)
Professor leonard
Contains
All classes
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