paulmcquad

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These are questions asked by paulmcquad

Hi,

I was hoping someone can tell me if there's a better way for doing this math.

I think i was doing this wrong so i posted the full results. The answers r correct but i might be doing this the long way.

Thanks in Advance.
 

Section 1.6: Combinations of Functions

 

Example 1: - Sum Rule

"ex1f(x):= 2 x+1"

proc (x) options operator, arrow, function_assign; 2*x+1 end proc

(1)

"ex1g(x):=x^(2)+2 x-1"

proc (x) options operator, arrow, function_assign; x^2+2*x-1 end proc

(2)

ex1f(x)+ex1g(x)

x^2+4*x

(3)

eval(x^2+4*x, [x = 2])

12

(4)

 

Example 2: - Difference Rule

"ex2f(x):=2 x+1"

proc (x) options operator, arrow, function_assign; 2*x+1 end proc

(5)

"ex2g(x):=x^(2)+2 x-1"

proc (x) options operator, arrow, function_assign; x^2+2*x-1 end proc

(6)

ex2f(x)-ex2g(x)

-x^2+2

(7)

eval(-x^2+2, [x = 2])

-2

(8)

Example 3: - Product Rule

"ex3f(x):=x^(2)"

proc (x) options operator, arrow, function_assign; x^2 end proc

(9)

"ex3g(x):= x-3"

proc (x) options operator, arrow, function_assign; x-3 end proc

(10)

ex3f(x)*ex3g(x)

x^2*(x-3)

(11)

collect(x^2*(x-3), x)

x^3-3*x^2

(12)

eval(x^3-3*x^2, [x = 4])

16

(13)

Example 4: - Quotient Rule

"ex4f(x):=sqrt(x)"

proc (x) options operator, arrow, function_assign; sqrt(x) end proc

(14)

"ex4g(x):=sqrt(4-x^(2))"

proc (x) options operator, arrow, function_assign; sqrt(4-x^2) end proc

(15)

ex4f(x)/ex4g(x)

x^(1/2)/(-x^2+4)^(1/2)

(16)

 

Example 5: - Composition - Chain Rule

 

This is an example of the chain rule.

"ex5t1(x):=sqrt(x):"

"ex5t2(x):=x-1:"

Function in another function:

 

ex5t1(ex5t2(x))

(x-1)^(1/2)

(1.1)

eval((x-1)^(1/2), [x = 2])

1

(1.2)

plot((x-1)^(1/2))

 

Example 6: - Composition - Chain Rule

 

Insert*two*functions

 

"ex6f(x):=x+2:"

"ex6g(x):=4-x^(2):"

 

ex6f(ex6g(x))

-x^2+6

(2.1)

eval(-x^2+6, [x = 0])

6

(2.2)

eval(-x^2+6, [x = 1])

5

(2.3)

``

ex6g(ex6f(x))

4-(x+2)^2

(2.4)

eval(4-(x+2)^2, [x = 0])

0

(2.5)

eval(4-(x+2)^2, [x = 1])

-5

(2.6)

``

Example 7: Find Domain with Chain Rule

 

Insert two Functions:

"ex7f(x):=x^(2)-9:"

"ex7g(x):=sqrt(9-x^(2)):"

``

ex7f(ex7g(x))

-x^2

(3.1)

plot(-x^2)

 

[-3, 3]

[-3, 3]

(3.2)

``


 

Download Ch1_6_Combo_Functions.mw

I don't know what's going wrong. It doesn't give a 2D Plot. Thanks in advance.

Temperature over 24hr period

 

y := 0.26e-1*x^3-1.03*x^2+10.2*x+34, 0 <= x and x <= 24

``

``

 

NULL


 

Download temperature24hr.mw

Hi, I would like to represent the piecewise function as a Bar Graph. I can only get a line Graph. Thanks in advance.
 

EXAMPLE 8 Interior Design Services Employees

 

"N(t):={[[-4.64 t +76.2 ,7<=t<=10],[0.90 t+20.0,11<=t<=12]]"

proc (t) options operator, arrow, function_assign; piecewise(7 <= t and t <= 10, -4.64*t+76.2, 11 <= t and t <= 12, .90*t+20.0) end proc

(1)

"->"

 

 

For 2007:

N(7) = 43.72 thousand employees

For 2011:

N(11) = 29.90 thousand employees``


 

Download Ch1_3_Functions_Exam8.mw

I'm trying to Graph a Piecewise Defined Function.

j(x) = piecewise(x < 0, x^2 + 1, 0 <= x, x - 1);

It doesn't provide a plot option.

Download piecewisegraph.mw


 

Function Misrepresented

y^2-x = 1"(->)"[[y = (x+1)^(1/2)], [y = -(x+1)^(1/2)]]NULL

NULL

 

Expected output for y

 

y = `&+-`(sqrt(1+x))

 

Yes it's the same meaning but i would like less to look at.


 

Download funct_misrep.mw

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