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Exercise

$\lim_{x,y\to0,\frac{\pi}{4}}\left(\sqrt{x^2+y^2+z^2}\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{y\to{0,\frac{\pi }{4}}}\left(\sqrt{x^2+y^2+z^2}\right)$ by replacing all occurrences of $y$ by $0,\frac{\pi }{4}$

$x,\sqrt{x^2+\left(0,\frac{\pi }{4}\right)^2+z^2}$

Final answer to the exercise

$x,\sqrt{x^2+\left(0,\frac{\pi }{4}\right)^2+z^2}$

Try other ways to solve this exercise

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  • Solve using limit properties
  • Solve using direct substitution
  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
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