Relations And Functions
Relations, 3 Quantitative Rulers, 4 Finite Numbers And Their
Neighborhoods, 6 Quantitative Screens, 8 Functions, 12 Functions
Specied By A Gl
From Local Graphs To
Smoothness, 55 -height Inputs, 57 Interpolation, 58 The
Essential Question, 60 The Essential Bounded Graph, 65 Essential
Notable Inputs, 67.
At the end of Chapter 1, we said that, a function being specied
local graph near
Graphic Local Analysis
Local Graphs, 37 Local Code, 38 Place of a Local Graph, 40
-Height Inputs and 0-Height Inputs, 42 Shape of a Local Graph, 44
Feature-Sign Change Inputs, 49 0-Slope and 0-Concavity Inputs, 51
Towards Local Analysis
Size Of Numbers, 23 Qualitative Rulers, 27 Dening large, small And
bounded, 28 Computing With large, small And bounded , 30 Innity,
32 Localization, 35.
Given that we will want to look
A) (- 3,0)
C) (0,- 3)
2) (9 , - 3)
The curve y =
, x 1 is revolved about the x-axis. Is the volume of the
resulting solid finite or infinite?
Solution. We apply the disks method and see that the question is about the
ln 2 x
convergence or divergence of the
Consider the region between curves y = cosh x, y = sinh x, x = 0, x = 1 .
1. Find the area of the region.
Solution. Recall that cosh x =
e x + e x
e x e x
and sinh x =
, whence sinh x cosh x .
Therefore the area is given by the
In problems 1 - 8 find the antiderivatives.
dx . We make the following substitution u = 2 x 6 + 1 . Then du = 12 x 5 dx and
therefore 3 x5 dx = du . After the substitution we get the following integral
and by P
Math 172 Review for the final exam.
1. Find the integrals.(8 points each) (a) x arctan x dx; Solution. We perform integration by parts taking u = arctan x and dv = xdx. Then du = Therefore x arctan x dx = = x2 1 arctan x- 2 2 = (b) 1 dt; + 2t + 2 Solution