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anonymous

  • one year ago

I have no idea how to solve this. Can someone please help me for a medal? :) (posting below)

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  1. anonymous
    • one year ago
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    \[\frac{ f(x+Δx)−f(x) }{ Δx }\] if f(x) = x^2

  2. IrishBoy123
    • one year ago
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    compute as \(\huge \frac{(x + \Delta x)^2 - x^2}{\Delta x}\)

  3. IrishBoy123
    • one year ago
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    so expand out the \(\large (x + \Delta x)^2\) in the numerator :p

  4. anonymous
    • one year ago
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    I know how to get to the expanding part, but I am not sure how to expand the numerator. Could you show me how?

  5. anonymous
    • one year ago
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    Would it end up looking like this... \[\frac{ x^{2} + Δx^{2}-x^{2} }{ Δx } \]

  6. IrishBoy123
    • one year ago
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    first expand out \( (x+Δx)^2\) on its own that's \( (x+Δx) \times (x+Δx)\)

  7. IrishBoy123
    • one year ago
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    |dw:1440705634106:dw|

  8. anonymous
    • one year ago
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    That makes sense, but how do you multiple an "Δx" by an "x"

  9. IrishBoy123
    • one year ago
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    \(x \times \Delta x = x \ \Delta x\)

  10. anonymous
    • one year ago
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    So the numerator would end up being... \[\frac{ x^{2}+2xΔx+Δx^{2}-x^{2} }{ Δx }\] which would simplify to... \[\frac{ 2xΔx+Δx^{2} }{ Δx }\] is that correct?

  11. IrishBoy123
    • one year ago
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    \[\checkmark\]

  12. IrishBoy123
    • one year ago
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    now finish it!

  13. anonymous
    • one year ago
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    \[\frac{ Δx(2x+Δx) }{ Δx }\] And the final answer would be... 2x+Δx ?

  14. IrishBoy123
    • one year ago
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    yay! well done learning calculus? happy days!

  15. anonymous
    • one year ago
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    Thank you so much. :)

  16. IrishBoy123
    • one year ago
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    any time! thank you.

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