Consider the following exercises: 1. What are the advantages of computing limit algebraically over using tables of values or graphs? 2. Give an example of a polynomial or rational function and de...

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Answer 1

Answer #1

1) If we compute the limit algebraically, we will get a definite answer rather than an approximation

2) If $x-2 x2-4 f(x)$ and we want to find $ェ→$

Cancelling terms, we can write this as $2 f(z) = Ina(1-2)( li + 2) = linz+2 = 4 r2 ( 2)(x +2)2+2 4$

3) In computing $lim f(x)$ if the denominator becomes zero, while the numerator is non-zero we can say the limit does not exist

If both numerator and denominator become zero, we can apply L'hospital's rule or do some kind of algebraic manipulation

4) $lim f(x)$ using graph, for example:

4 N f(x)=岩 x=2 2 10 -10 (2,0.25) Label: (2, 0.25) 3 0 -2 -3

Here, we draw the graph and find the limit by noting the value of the function close to the point under consideration

$lim f(x)$ using algebraic manipulation as above:

$2 f(z) = Ina(1-2)( li + 2) = linz+2 = 4 r2 ( 2)(x +2)2+2 4$

$lim f(x)$ using L'hospital's rule

Since $lim(x - 2)lim(r24)0$ we have

$2 lim 1-2 (12-1), lim f(x) = lim r→2 r-2 (2-2) (2+ 2) 2 (x2-4)+2 2x4 1-2 2x$

Answer 2