Question

Is the following true?

*mathematical terms in first comment*

Thank you very much! Any and all help is greatly appreciated!

Answer 1

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

Answer 2

Is this a way to evaluate this?

Answer 3

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.

Answer 4

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? :/

Answer 5

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

Answer 6

the algebra is messy but it should work

Answer 7

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! :(

Answer 8

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

Answer 9

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.