Given `lim_(x->-2) f(x)=5` and `lim_(x->-2) g(x)=5` , evaluate: `lim_(x->-2) [f(x)-g(x)]`

all limits are as x approaces -2

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You need to use the following identity such that:

`lim_(x->x_0) (f(x) - g(x)) = lim_(x->x_0) (f(x)) - lim_(x->x_0) (g(x))`

Since the problem provides the information that `lim_(x->-2)(f(x)) = 5` and `lim_(x->-2)(g(x)) = 5` , yields:

`lim_(x->-2) (f(x) - g(x)) = 5 - 5`

`lim_(x->-2) (f(x) - g(x)) = 0`

**Hence, evaluating the limit, under the given conditions, yields **`lim_(x->-2) (f(x) - g(x)) = 0.`

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