The function $$g$$ is defined over the real numbers. This table gives a few values of $$g$$.

![](http://admin.getprephub.com/media/editor/l3_20220921223432900133.png)
What is a reasonable estimate for $$\lim _{x \to -2} g(x) ?$$ 

<div id="displayOption3" class="markdown-body editormd-html-preview"><textarea>limit does not exceed</textarea>limit does not exceed
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<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea>The function $$g$$ is defined over the real numbers. This table gives a few values of $$g$$.

![](http://admin.getprephub.com/media/editor/l3_20220921223432900133.png)
What is a reasonable estimate for $$\lim _{x \to -2} g(x) ?$$ </textarea>The function <math><semantics><mrow><mi>g</mi></mrow><annotation encoding="application/x-tex">g</annotation></semantics></math>g is defined over the real numbers. This table gives a few values of <math><semantics><mrow><mi>g</mi></mrow><annotation encoding="application/x-tex">g</annotation></semantics></math>g.
<img src="http://admin.getprephub.com/media/editor/l3_20220921223432900133.png" alt=""> What is a reasonable estimate for <math><semantics><mrow><msub><mi>lim</mi><mrow><mi>x</mi><mo>→</mo><mo>−</mo><mn>2</mn></mrow></msub><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>?</mo></mrow><annotation encoding="application/x-tex">\lim _{x \to -2} g(x) ?</annotation></semantics></math>lim​x→−2​​g(x)? 
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<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea>
$$g(x)$$ values seem to approach a distinct value as $$x$$ approach $$-2$$.
![](http://admin.getprephub.com/media/editor/Screenshot%202022-09-22%20130600_20220922073613102328.png)
As $$x$$ increases towards $$-2$$, $$g(x)$$ values seem to approach $$8$$.
![](http://admin.getprephub.com/media/editor/Screenshot%202022-09-22%20131722_20220922074731274680.png)
As $$x$$ deereases towards $$x=-2$$, the values of g(x)$$ seem to apporoach 8 .

$$\therefore \lim _{x \to -2} g(x) ?=8$$ 

</textarea><math><semantics><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">g(x)</annotation></semantics></math>g(x) values seem to approach a distinct value as <math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math>x approach <math><semantics><mrow><mo>−</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">-2</annotation></semantics></math>−2. <img src="http://admin.getprephub.com/media/editor/Screenshot%202022-09-22%20130600_20220922073613102328.png" alt=""> As <math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math>x increases towards <math><semantics><mrow><mo>−</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">-2</annotation></semantics></math>−2, <math><semantics><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">g(x)</annotation></semantics></math>g(x) values seem to approach <math><semantics><mrow><mn>8</mn></mrow><annotation encoding="application/x-tex">8</annotation></semantics></math>8. <img src="http://admin.getprephub.com/media/editor/Screenshot%202022-09-22%20131722_20220922074731274680.png" alt=""> As <math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math>x deereases towards <math><semantics><mrow><mi>x</mi><mo>=</mo><mo>−</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">x=-2</annotation></semantics></math>x=−2, the values of g(x)$$ seem to apporoach 8 .
<math><semantics><mrow><mo>∴</mo><msub><mi>lim</mi><mrow><mi>x</mi><mo>→</mo><mo>−</mo><mn>2</mn></mrow></msub><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>?</mo><mo>=</mo><mn>8</mn></mrow><annotation encoding="application/x-tex">\therefore \lim _{x \to -2} g(x) ?=8</annotation></semantics></math>∴lim​x→−2​​g(x)?=8 
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