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

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

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