Chapter 5: Getting Closer and Closer 

Math Problem Set 

1.        Numerically determine 

LeftSide := [-0.1e-1, -0.1e-2, -0.1e-3];  

LeftSide := [-0.1e-1, -0.1e-2, -0.1e-3]; (5.1.1)
 

RightSide := [0.1e-1, 0.1e-2, 0.1e-3];  

RightSide := [0.1e-1, 0.1e-2, 0.1e-3]; (5.1.2)
 

f := proc (x) options operator, arrow, function_assign; `/`(`*`(sin(x)), `*`(x)) end proc;  

f := proc (x) options operator, arrow; `/`(`*`(sin(x)), `*`(x)) end proc; (5.1.3)
 

map(f, LeftSide);  

[.9999833334, .9999998333, .9999999983]; (5.1.4)
 

map(f, RightSide);  

[.9999833334, .9999998333, .9999999983]; (5.1.5)
 

 

 

 

`/`(`*`(sin(x)), `*`(x)); f(x); 1.000000000;  

 

 

 

 

2.        Consider f(x) = `/`(`*`(sin(x)), `*`(x)); .  Does it have a discontinuity? Create a plot. If a discontinuity exists, highlight it on the image.  

3.        Determinelimit(`/`(`*`(sin(x)), `*`(x)), x = 0); using the limit() command.  

4.        Given that `and`(`<=`(cos(x), `/`(`*`(sin(x)), `*`(x))), `<=`(`/`(`*`(sin(x)), `*`(x)), 1)); -1 

5.        Evaluate the limit or determine that it does not exist. State a reason why. Use a graph to back up all conclusions.  

6.        Determine what value of the constant ‘ a ‘ makes the function  f(x) = piecewise(`<=`(1, x), `+`(`*`(3, `*`(`^`(x, 2)))), `<`(x, 1), `+`(`*`(a, `*`(x)), `-`(4))); continuous everywhere. 

7. Determine the equation of a function where the following conditions are met:  

8.          Using the Limit Tutor determine: `+`(sqrt(`+`(`*`(a, `*`(x)), `*`(`^`(x, 2)))), `-`(sqrt(`+`(`*`(b, `*`(x)), `*`(`^`(x, 2))))));
 

Maple Problem Set