A function f is given by f ( x ) = 1 ( x − 5 ) 2 . This function takes a number x , subtracts 5 from it, squares the result, and takes the reciprocal of the square. a. Find f ( 3 ) , f ( − 1 ) , f ( k ) , f ( t − 1 ) , f ( t − 4 ) , and f ( x + h ) . b. Note that f could also be given by f ( x ) = 1 x 2 − 10 x + 25 . Explain what this does to an input number x .
A function f is given by f ( x ) = 1 ( x − 5 ) 2 . This function takes a number x , subtracts 5 from it, squares the result, and takes the reciprocal of the square. a. Find f ( 3 ) , f ( − 1 ) , f ( k ) , f ( t − 1 ) , f ( t − 4 ) , and f ( x + h ) . b. Note that f could also be given by f ( x ) = 1 x 2 − 10 x + 25 . Explain what this does to an input number x .
Solution Summary: The author explains how to calculate the function f(x)=12 for various values of x.
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY