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andreyandreev [35.5K]
3 years ago
12

Look in attachment ..answer if u know only pls

Mathematics
1 answer:
timurjin [86]3 years ago
3 0
First of all, you have to understand g<span> is a square-root function. 

</span>Square-root functions are continuous across their entire domain, and their domain is all real x-<span>values for which the expression within the square-root is non-negative. 
</span>
In other words, for any square-root function q and any input c in the domain of q (except for its endpoint), we know that this equality holds:  lim \ q(x)=q(c) 

Let's take \sqrt{x} <span>as an example. 
</span>
The domain of \sqrt x is all real numbers such that x \geq 0.  Since x=0  is the endpoint of the domain, the two-sided limit at that point doesn't exist (you can't approach 0 <span>from the left). 
</span>
<span>However, continuity at an endpoint only demands that the one-sided limit is equal to the function's value: 
</span>
lim \  \sqrt{x} =  \sqrt{0} =0 

In conclusion, the equality lim \ q(x)=q(c) holds for any square-root function q and any real number c  in the domain of q e<span>xcept for its endpoint, where the two-sided limit should be replaced with a one-sided limit. </span>

The input x=-3,  is within the domain of g<span>. 
</span>
Therefore, in order to find  lim \ g(x)  we can simply evaluate g at x-3<span>. 
</span>
g(x) 

\sqrt{7x+22} 

\sqrt{7(-3)+22} 

\sqrt{1} =1
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