april1renee
f(x)=5x^2 f(x+h)-f(x)/h
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Jonask
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f(x+h) means where you see the x you add h DO NOT FOCUS ON OTHER NUMBERS
Zelda
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10x Should be the final answer.
Jonask
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@Zelda theres no limit here
april1renee
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5(x+h)^2 -f(5x^2) ??
Jonask
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yes then divide by h
april1renee
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5(x^2+2xh+h^2)= 5x^2+10xh+5h^2
april1renee
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5x^2+10x+5h
Zelda
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Hey april, is there the word lim as h-> 0 before f(x)?
Jonask
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5x^2+10xh+5h^2-(5x^2+10x+5h)=
april1renee
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the answer i have is 10x+5h
Jonask
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yes but is there any thing like this \[\lim_{h \rightarrow 0}\] on the question
april1renee
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no
april1renee
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professor answer is 5(2x+h) i dont undestand why i would divide by 5
ZeHanz
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It would be (very much) more clear if everyone wouldn't just write peaces of the problem, but the whole thing:\[\frac{ f(x+h)-f(x) }{ h }=\frac{ 5(x+h)^2-5x^2 }{ h }=\frac{ 5(x^2+2xh+h^2)-5x^2 }{ h }\]See? Just keep on writing the complete fraction, simpifying it along the way, until you're done:\[\frac{ 5x^2+10xh+5h^2-5x^2 }{ h }=\frac{ 10xh+5h^2 }{ h }=\frac{ 5h(2x+h) }{ h }=5(2x+h)\]So finally we've lost the fraction!
Sooner or later the question of what will happen if h goes to 0 will be asked.
Here you see immediately that leads to 10x.
ZeHanz
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Of course, you could write the answer also as 10x + 5h
april1renee
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THANK YOU!
ZeHanz
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You're welcome!