What is the limit as x approaches 2 of 1/(g(x)+2) ?

The limit as x approaches 2 of 1/(g(x)+2) is 1/(g(2)+2)

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limit as x approaches 2 of 1/(g(x)+2)

x \to 2 lim (\frac{1}{g ( x ) + 2})

\frac{1}{g ( 2 ) + 2}

Solution steps

x \to 2 lim (\frac{1}{g ( x ) + 2})

Plug in the value

x = 2

, assuming the function is continuous at this point

= \frac{1}{g ( 2 ) + 2}

x \to 0 lim (x sin (\frac{1}{2 x}))

x \to \infty lim ((\frac{1}{2})^{\infty})

x \to - 3 lim (\frac{2 x - 6}{x + 3})

x \to 0 lim (\frac{e ^{x}}{2 x})

x \to - 2 + lim (\frac{x ^{2}}{x ^{2} - 4})

What is the limit as x approaches 2 of 1/(g(x)+2) ?
The limit as x approaches 2 of 1/(g(x)+2) is 1/(g(2)+2)