Wolfram Alpha Project M071 F12 25 points Due Wed. Dec. 5 Name_____________________________
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 output. The easiest way to do this is to download this word document from my web site
http://www.math.sjsu.edu/~foster/m071/m071fall12.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 output 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 5.
For your reference related examples using Wolfram Alpha are at my 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
𝑥 3 +4𝑥 2 +5𝑥+6
𝑥+3
(2) Wolfram Alpha input:
(3) Wolfram Alpha output:
2.
Calculate a derivative.
(1) Original problem:
𝑑 √𝑥 2 +5√𝑥 2 +1
(𝑥 2 +2)
𝑑𝑥
(2) Wolfram Alpha input:
(3) Wolfram Alpha output:
3.
Find the slope of a tangent line:
(1) Original problem: find the slope of the tangent line to y=
√(𝑥 2 +5) √(𝑥 2 +1)
(𝑥 2 +2)
at x=2
(2) Wolfram Alpha input:
(3) Wolfram Alpha output:
4.
Find a second derivative.
(1) Original problem:
𝑑 2 √𝑥 2 +5√𝑥 2 +1
𝑑𝑥 2
(𝑥 2 +2)
(2) Wolfram Alpha input:
(3) Wolfram Alpha output:
5.
Implicit differentiation.
(1) Original problem: Find
𝑑𝑦
𝑑𝑥
if 𝑥 4 𝑦 2 + 4𝑥𝑦 2 = 𝑥
(2) Wolfram Alpha input:
(3) Wolfram Alpha output:
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 output:
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 output:
8.
Indefinite integral
𝑒 𝑥 −𝑒 −𝑥
(1) Original problem: find the indefinite integral ∫ (𝑒 −𝑥
+𝑒 𝑥 )2
𝑑𝑥
(2) Wolfram Alpha input:
(3) Wolfram Alpha output:
9.
Definite integral
2 𝑒 𝑥 −𝑒 −𝑥
(1) Original problem: find the indefinite integral∫0
(𝑒 −𝑥 +𝑒 𝑥 )2
𝑑𝑥
(2) Wolfram Alpha input:
(3) Wolfram Alpha output:
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 output (3-D plot and Contour Plot):
11. Partial derivatives
(1) Original problem: evaluate
𝜕2 𝑓
𝜕𝑥𝜕𝑦
or 𝑓𝑥𝑦 for 𝑓(𝑥, 𝑦) = 𝑒 𝑥 ln(𝑥 + 𝑦)
(2) Wolfram Alpha input:
(3) Wolfram Alpha output:
12. Solution to a Lagrange multiplier problem
(1) Original problem: use Lagrange multipliers to minimize 𝑥 2 + 𝑦 2 + 𝑧 2 with the restriction that (x,y,z) is on
the sphere (𝑥 − 3)2 + (𝑦 − 4)2 + (𝑧 − 12)2 − 676 = 0 . This finds the point on the sphere that is closest to
the origin.
(2) Wolfram Alpha input :
(3) Wolfram Alpha output:
(4) Answer to minimization problem.:
13. 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 output.
(1) Original problem:
(2) Wolfram Alpha input:
(3) Wolfram Alpha output: