Wolfram Alpha Project M071 F14 25 points Due Monday Dec. 8 Name_____________________________
Updated 11-23-2014
For each of the following parts (except for the last part) a problem is listed. Solve each problem using Wolfram
Alpha. For each problem add to this word document your Wolfram Alpha input for the problem and the Wolfram
Alpha result. The easiest way to do this is to download this word document from my web site
http://www.math.sjsu.edu/~foster/m071_f14/m071fall14.html and then to cut and paste your answers from
Wolfram Alpha to the word document. To cut / paste answers from Wolfram Alpha (a) right click on the Wolfram
result in your browser, (b) select copy image, (c) move to MS word and paste (ctrl V). Turn in a printed copy of the
modified word document at the beginning of class on December 8.
For your reference related examples using Wolfram Alpha are at the course web page. Wolfram Alpha is available
at http://www.wolframalpha.com/. It can be accessed using any internet browser. There are also I-phone and
Android apps to access Wolfram Alpha. However, unless your smart phone has MS word (so that you can add to
this document), you will probably need to use a computer browser.
1.
Find a limit.
(1) Original problem: lim𝑥→−3
(2) Wolfram Alpha input:
(3) Wolfram Alpha result:
2.
𝑥+3
Calculate a derivative.
(1) Original problem:
𝑑 �𝑥 2 +5�𝑥 2 +1
𝑑𝑥
(2) Wolfram Alpha input:
(3) Wolfram Alpha result:
3.
𝑥 3 +4𝑥 2 +5𝑥+6
(𝑥 2 +2)
Find the slope of a tangent line:
(1) Original problem: find the slope of the tangent line to y=
(2) Wolfram Alpha input:
(3) Wolfram Alpha result:
4.
Find a second derivative.
(1) Original problem:
𝑑 2 �𝑥 2 +5�𝑥 2 +1
𝑑𝑥 2
(2) Wolfram Alpha input:
(3) Wolfram Alpha result:
(𝑥 2 +2)
5. Solve the system of equations.
(1) Original problem: solve the system:
(2) Wolfram Alpha input:
(3) Wolfram Alpha result:
x + 2 y + z + w = 12
x − y + 2z + w = 9
3x + y − z + 2w = 10
2 x − y + 3z − w = 5
�(𝑥 2 +5) �(𝑥 2 +1)
(𝑥 2 +2)
at x=2
6.
Critical numbers.
(1) Original problem: Find the critical numbers of 𝑓(𝑥) = 3𝑥 4 + 8𝑥 3 − 30 𝑥 2 − 72 𝑥
(2) Wolfram Alpha input:
(3) Wolfram Alpha result:
7.
Draw a plot of a function.
(1) Original problem: draw a plot of the function 𝑓(𝑥) = 3𝑥 4 + 8𝑥 3 − 30 𝑥 2 − 72 𝑥
(2) Wolfram Alpha input:
(3) Wolfram Alpha result:
8.
Indefinite integral
𝑒 𝑥 −𝑒 −𝑥
(1) Original problem: find the indefinite integral ∫ (𝑒 −𝑥
(2) Wolfram Alpha input:
(3) Wolfram Alpha result:
9.
+𝑒 𝑥 )2
𝑑𝑥
Definite integral
2 𝑒 𝑥 −𝑒 −𝑥
(1) Original problem: find the indefinite integral∫0
(2) Wolfram Alpha input:
(3) Wolfram Alpha result:
(𝑒 −𝑥 +𝑒 𝑥 )2
𝑑𝑥
10. Plot a surface and a contour plot
(1) Original problem: draw a plot of the surface 𝑓(𝑥, 𝑦) = 𝑥 2 𝑦 + 2𝑥 2 + 2𝑦 3 + 11𝑦 2 + 16𝑦 + 7 in three
dimensions and draw a contour plot in 2 dimensions
(2) Wolfram Alpha input:
(3) Wolfram Alpha result (3-D plot and Contour Plot):
11. Partial derivatives
(1) Original problem: evaluate
(2) Wolfram Alpha input:
(3) Wolfram Alpha result:
𝜕2 𝑓
𝜕𝑥𝜕𝑦
or 𝑓𝑥𝑦 for 𝑓(𝑥, 𝑦) = 𝑒 𝑥 ln (𝑥 + 𝑦)
12. Solve a problem of your choice (not one of the above problems) using Wolfram Alpha. This could be any math
problem on a topic that we studied or on a topic that we did not study, or it could be a problem related to any of
the applications mentioned at http://www.wolframalpha.com/examples/ or a link at that web site. List the
problem (this could be entered by hand or typed in), the Wolfram Alpha input and the Wolfram Alpha result.
(1) Original problem:
(2) Wolfram Alpha input:
(3) Wolfram Alpha result: