 The function $$h$$ is defined for all real numbers except for $$x=0$$. What is a reasonable estimate for $$\lim_{x \to 0} h(x)$$ ?

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<div id="displayOption0" class="markdown-body editormd-html-preview"><textarea>limit does not exist</textarea>limit does not exist
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<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea> The function $$h$$ is defined for all real numbers except for $$x=0$$. What is a reasonable estimate for $$\lim_{x \to 0} h(x)$$ ?

![](http://admin.getprephub.com/media/editor/l7_20220921223930493827.png)</textarea> The function <math><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math>h is defined for all real numbers except for <math><semantics><mrow><mi>x</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">x=0</annotation></semantics></math>x=0. What is a reasonable estimate for <math><semantics><mrow><msub><mi>lim</mi><mrow><mi>x</mi><mo>→</mo><mn>0</mn></mrow></msub><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">\lim_{x \to 0} h(x)</annotation></semantics></math>lim​x→0​​h(x) ?
<img src="http://admin.getprephub.com/media/editor/l7_20220921223930493827.png" alt="">
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<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea>From the graph, $$f(x)$$ does not exist at $$x=0$$ 
When $$x \to 0^{+} ,f(x)$$ apperoaches $$+\infty$$
When $$x \to 0^{-} ,f(x)$$ apperoaches $$-\infty$$

$$\therefore$$ limit does not exist


</textarea>From the graph, <math><semantics><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">f(x)</annotation></semantics></math>f(x) does not exist at <math><semantics><mrow><mi>x</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">x=0</annotation></semantics></math>x=0 When <math><semantics><mrow><mi>x</mi><mo>→</mo><msup><mn>0</mn><mrow><mo>+</mo></mrow></msup><mo separator="true">,</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">x \to 0^{+} ,f(x)</annotation></semantics></math>x→0​+​​,f(x) apperoaches <math><semantics><mrow><mo>+</mo><mi mathvariant="normal">∞</mi></mrow><annotation encoding="application/x-tex">+\infty</annotation></semantics></math>+∞ When <math><semantics><mrow><mi>x</mi><mo>→</mo><msup><mn>0</mn><mrow><mo>−</mo></mrow></msup><mo separator="true">,</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">x \to 0^{-} ,f(x)</annotation></semantics></math>x→0​−​​,f(x) apperoaches <math><semantics><mrow><mo>−</mo><mi mathvariant="normal">∞</mi></mrow><annotation encoding="application/x-tex">-\infty</annotation></semantics></math>−∞
<math><semantics><mrow><mo>∴</mo></mrow><annotation encoding="application/x-tex">\therefore</annotation></semantics></math>∴ limit does not exist
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