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

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

Calculus1
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[\lim_{h \rightarrow 0}100+50x-4.9x^2 = \lim_{h \rightarrow 0}100 +\lim_{h \rightarrow 0}50x - \lim_{h \rightarrow 0}4.9x^2 \]
Is this a way to evaluate this?
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.

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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? :/
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
the algebra is messy but it should work
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! :(
not sure what "a" is referring to, can you be more specific?
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.

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