## amonoconnor one year ago Is the following true? *mathematical terms in first comment* Thank you very much! Any and all help is greatly appreciated!

1. amonoconnor

$\lim_{h \rightarrow 0}100+50x-4.9x^2 = \lim_{h \rightarrow 0}100 +\lim_{h \rightarrow 0}50x - \lim_{h \rightarrow 0}4.9x^2$

2. amonoconnor

Is this a way to evaluate this?

3. Vocaloid

yes, you can evaluate it, but there's no need to in this case. one of the rules of limits is that you can "split" the limit like it's been done above.

4. amonoconnor

When I used the limit method to find the derivative of the whole expression, I got stuck, and couldn't find a way to simplify it... can you show me how you would do it without expanding? :/

5. Vocaloid

let f(x) = 100 + 50x - 4.9x^2 evaluate limit h --> 0 for [ f(x+h) - f(x) ] / h that should give the same result (the derivative) as splitting the limit up

6. Vocaloid

the algebra is messy but it should work

7. amonoconnor

Do I plug in the value I was given as "a" for x on like the second step, or is it proper to keep this out and plug in a number only once I'm done "deriving". This is where I got stuck before, because I kept it out, and then had a bunch of h terms, a bunch of x terms, and then 100. And I didn't know what to do! :(

8. Vocaloid

not sure what "a" is referring to, can you be more specific?

9. amonoconnor

Yeah, sorry about that! I was given "x=5", as a 'time' for when I'm supposed to analyze for the velocity, given through the derivative of f(x)=100+50x+4.9t^2. I'm supposed to use the limit method to get the derivative as well, I'm not allowed to use the Power Rule.