Explain the advantages and disadvantages of a graphing calculator to find or check the solution of an equation

Question

Can anyone answer it? I have it as a question for math.

Answer 1

The advantage is that it can be done mechanically, with no insight or intelligence of any sort, it can be used to find (approximate) solutions for any equation, no matter how complicated (given that even something as simple as a quintic polynomial cannot always have its solutions expressed using a finite number of field operations and root extractions, approximate solutions are sometimes the best you can do), and if being used to check solutions, minimizes the chance of arithmetical error in the verification. It can also be used to assist in the visualization of a function (although cannot replace it, since somtimes a function has irregularities on a scale smaller than the pixels of the graph window).

The disadvantages are that since the graphing calculator works numerically rather than symbolically, it sometimes accumulates serious numerical errors from rounding (compare http://img206.imageshack.us/img206/1730/graph1nv6.png with http://img205.imageshack.us/img205/7366/graph2gw6.png -- these two should be the same polynomial, but the second doesn't look like a polynomial at all because of numerical instability in the calculation). Also, it can give misleading solutions (do not EVER try to find the limit of a function using a calculator unless you know before you enter the function what the graph looks like -- I've seen too many students get burned because the behavior of a function changes just outside their graph window, or on a scale too small to see), and frequently can only verify that a solution is correct to within some numerical error -- a verification that the solution is actually exactly correct requires symbolic manipulation. Finally, attempting to use the graphing calculator constantly will lead to the atrophy of symbolic manipulation skills, typically rendering it inappropriate for use in a math class, whose purpose is to develop those skills. This is not to say that the calculator should never be used in math class, but if the students are using it to do mathematics rather than computation, they invariably end up failing in later courses where success is impossible without actual understanding (taken any analysis courses lately?).

Answer 2

too expensive, but i used it alot in college