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

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jmg5639 | Student, Undergraduate | Honors

Posted January 20, 2013 at 3:30 PM via web

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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

Tagged with calculus, math

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted January 20, 2013 at 3:39 PM (Answer #1)

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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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