What is the limit as x approaches 3 of x/((x^2+y^2)) ?

The limit as x approaches 3 of x/((x^2+y^2)) is 3/(9+y^2)

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limit as x approaches 3 of x/((x^2+y^2))

x \to 3 lim (\frac{x}{( x ^{2} + y ^{2} )})

\frac{3}{9 + y ^{2}}

Solution steps

x \to 3 lim (\frac{x}{x ^{2} + y ^{2}})

Plug in the value

x = 3

= \frac{3}{3 ^{2} + y ^{2}}

Simplify

= \frac{3}{9 + y ^{2}}

x \to 3 lim (\frac{x}{x - 1})

x \to 3 lim (x^{2} - x^{2} cos (x))

x \to 3 lim (ln (\frac{1 + 1}{x}))

x \to 3 lim (\frac{x ^{2}}{x !})

x \to 3 lim (x^{3} e^{- x})

What is the limit as x approaches 3 of x/((x^2+y^2)) ?
The limit as x approaches 3 of x/((x^2+y^2)) is 3/(9+y^2)