Project 3,Math 1132 Name:_________________________
Fall 2002, Dr.Howard
Use this as acover sheet for your project.
Evaluating Limits with Maple.
Maple has the built-in capability to evaluate limits.For example,to evaluate the one-sided limit
lim
x→0+x1/xwith Maple,one can enter the statement
>limit(x^(1/x), x=0,right );
and Maple will evaluate the limit.(You should start Maple and enter the above statement to see for
yourself).For limits that are not one-sided limits,simply omit the optional part of the statment
(right)and the preceding comma.
Of course,there are other ways to see that zero is the value of the limit above.For example,one
can define and graph the associated function over asuitable interval:
>f:=x->x^(1/x);
>plot(f(x), x=0.0001..1);
One also might simply evaluate the function at selected numbers to make atable and see that the
values of f(x)approach zero as xapproaches zero:
>f(0.5);
>f(0.1);
>f(0.01);
Evaluating Derivatives With Maple.
To apply L’Hopital’sRule with Maple,you will need to take some derivatives.To take the
derivative of tan sin3x
x5−lnx,for example,you can enter the following statements in Maple.
>f:=x->tan(sin(3*x)/(x^5-ln(x) );
>diff(f(x), x);
Instructions for your assignment (Due Nov.11).
For each limit described below,find the limit in each of the following ways:
a.Apply L’Hopital’srule and appropriate hand computations to determine the limit (you may use
Maple to evaluate derivatives if you wish).
b. Draw an appropriate graph over an appropriate interval to visually illustrate the limit.
c.Use Maple and the limit statement to evaluate the limit.
1.lim
x→0+−xlnx
2.lim
x→0
ex−(1+x)
x2[Remember to use exp(x)in Maple for ex]
3.lim
x→∞1+2
xx
1