FUNCTION:LIMITS

Posted by : Allan_Dell on Friday, March 6, 2020 | 7:59 AM

Limits

Treating this problem is by simply substitution. Not really that hard. Just stick with the given equation and look what to find with regards to the system flow given. Illustrations and more examples were provided to further understand the operations. In the provided illustrations, numbers 1 to 3 are seems easy, and gradually challenging from 4 to 5. See how the answers varies from different unknown functions? In "More examples", the values of x "were" highlighted just to have an "easy glance" if in case you're about to confuse. Sometimes if we stuck, it is so annoying looking what must to find if they are in the series. Answers were highlighted in green to let you know that's the end for final answer. Some answers from "Illustrations" and "more examples" can still be factored out, (see all on "more examples", you can put the answers in factored-out form in the comment box if you got it). In the "Challenge yourself" section, it is by the authors intention not to provide an answer. Your answer must put in the comment box and let see how is it done. I can give the right answer if I found your answer wrong.

Illustrations:

Perform the indicated operations for the given functions.

Given that $f(x)=x^{2}-x+3$ , find f(0), f(2), f(-4), f(-2x), f(3x), f $(3x^{2})$

Solution:

$1. f(x)=x^{2}-x+3$
$f(0)=0^{2}-0+3$
$f(0)=3$

$2. f(x)=x^{2}-x+3$
$f(2)=(2)^{2}-2+3$
$f(2)=5$

$3. f(x)=x^{2} -x+3$
$f(-4)=(-4)^{2} -(-4)+3$
$f(-4)=16+4+3=23$

$4.f(x)=x^{2}-x+3$
$f(-2x)=(-2x)^{2}-(-2x)+3$
$f(-2x)=4x^{2}+2x+3$

$5. f(x)=x^{2}-x+3$
$f(3x^{2})=(3x^{2})^{2}-(3x^{{2}})+3$
$f(3x^{2})=9x^{4}-3x^{{2}}+3$

More examples:

If, $f(x)=6+2x-x^{2}$ , Find $f(5b), f(-3a),f(-2y)$ .

Solution:

$a.) f(x)=6+2x-x^{2}, {\color{Red} x=5b}$
$f(5b)=6+2(5b)-(5b)^{2}$
$f(5b)=6+10b-25b^{2}, {\color{DarkGreen} ans.}$

$b.)f(x)=6+2x-x^{2}, {\color{Red} x{\color{Red} }=-3a}$
$f(-3a)=6+2(-3a)-(-3a)^{2}$
$f(-3a)=6-6-9a^{2},{\color{DarkGreen} ans{\color{DarkGreen} }}$

$c.)f(x)=6+2x-x^{2},{\color{Red} x=-2y}$
$f(-2y)=6+2(-2y)-(-2y)^{2}$
$f(-2y)=6-4y-4y^{2}, {\color{DarkGreen} ans}$