Evaluating the Limit of (x+2)/((√(x^2-4))) as x approaches 2

Evaluate the limit Lim (x+2)/((√x^2-4))x→2

To evaluate the limit, we can directly substitute the value of x=2 into the given expression and simplify:

Lim (x+2)/((√(x^2-4))) as x approaches 2

Plugging in x=2, we get:

Lim (2+2)/((√(2^2-4)))
= Lim (4)/(√(4-4))
= Lim (4)/(√(0))

Now, we have a division by zero situation in the denominator

To evaluate the limit, we can directly substitute the value of x=2 into the given expression and simplify:

Lim (x+2)/((√(x^2-4))) as x approaches 2

Plugging in x=2, we get:

Lim (2+2)/((√(2^2-4)))
= Lim (4)/(√(4-4))
= Lim (4)/(√(0))

Now, we have a division by zero situation in the denominator. This means the limit is undefined, as the expression approaches infinity.

Therefore, the limit Lim (x+2)/((√x^2-4)) as x approaches 2 is undefined.

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