compton7551 compton7551
  • 21-09-2018
  • Mathematics
contestada

Find the limit, if it exists. (if an answer does not exist, enter dne.) lim (x, y)→(0, 0) x10 − y10 x5 y5

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Аноним Аноним
  • 01-10-2018

The function is [tex]Limit \text (x,y)→ (0,0) \frac{{x^{10} -y^{10}}}{x^5-y^5}[/tex]

 ⇒[tex]Lim(x,y)\rightarrow (0,0)\frac{{x^5}^2-{y^5}^2}{{x^5-y^5}}[/tex]

→[tex]Lim(x,y)\rightarrow (0,0)\frac{(x^5-y^5)\times(x^5+y^5)}{(x^5-y^5)}[/tex]

 ∵ As you must have learned in your middle school that (A^2 -B^2)=(A-B)(A+B)

→[tex]Lim(x,y)\rightarrow (0,0){(x^5+y^5)}[/tex]

 =0+0

=0

Hence the value of the given function i.e [tex]\frac{{x^{10} -y^{10}}}{x^5-y^5}[/tex] when (x,y)→(0,0) is 0.

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