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april1renee

  • 3 years ago

f(x)=5x^2 f(x+h)-f(x)/h

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  1. Jonask
    • 3 years ago
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    f(x+h) means where you see the x you add h DO NOT FOCUS ON OTHER NUMBERS

  2. Zelda
    • 3 years ago
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    10x Should be the final answer.

  3. Jonask
    • 3 years ago
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    @Zelda theres no limit here

  4. april1renee
    • 3 years ago
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    5(x+h)^2 -f(5x^2) ??

  5. Jonask
    • 3 years ago
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    yes then divide by h

  6. april1renee
    • 3 years ago
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    5(x^2+2xh+h^2)= 5x^2+10xh+5h^2

  7. april1renee
    • 3 years ago
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    5x^2+10x+5h

  8. Zelda
    • 3 years ago
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    Hey april, is there the word lim as h-> 0 before f(x)?

  9. Jonask
    • 3 years ago
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    5x^2+10xh+5h^2-(5x^2+10x+5h)=

  10. april1renee
    • 3 years ago
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    the answer i have is 10x+5h

  11. Jonask
    • 3 years ago
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    yes but is there any thing like this \[\lim_{h \rightarrow 0}\] on the question

  12. april1renee
    • 3 years ago
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    no

  13. april1renee
    • 3 years ago
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    professor answer is 5(2x+h) i dont undestand why i would divide by 5

  14. ZeHanz
    • 3 years ago
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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.

  15. ZeHanz
    • 3 years ago
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    Of course, you could write the answer also as 10x + 5h

  16. april1renee
    • 3 years ago
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    THANK YOU!

  17. ZeHanz
    • 3 years ago
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    You're welcome!

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