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This is problem number sixty five of this tour Calculus
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eighth edition, Section two point six. Use the
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squeeze staring to evaluate the Limited's expertise in penalty.
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A sign of X over Now are squeezed there,
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Miss Cui recall is if we have two three functions
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age Afrin, G and F is a function that
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is greater than or equal to h but less than
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or equal to G and the limit as experts.
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Zane, some value ain of age is equal to
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the limit. Is expert is eight for the function
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gene, and this is they're both equal to each
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other to some limit at all. Therefore, for
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these reasons, the result is that the limit is
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expert is a for the function have it is also
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equal down and that is the definition of are squeezed
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here. Um, we're going do this for our
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problem here. Com. We know that sign of
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X is a function that arse awaits between the values
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negative or a positive one. If we divide each
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turn by X, we get negative. Wanna Rex
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less than equal to sign X or ex less than
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equal to one a rex. And now, if
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we just take the limit. Ah, Of each
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term as ex president, well has expressions impunity for
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negative One of rags approaches zero since a very large
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number of the denominator it means of this number increasingly
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grows smaller. So the limit hero be zero.
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The same reasoning goes to proving that the limit its
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export is infinity. One over hex goes through.
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So that must mean they're because the planet is expressive
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unity of negative Wanna wreck zero And the Limited Express
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in India won a rec zero. Then the limited
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Express infinity of sand over Cenex Rex must also be
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zero. All right, preppie graph vexes sine x
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rex. How many times is a graft crosses the
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asked me to So when it talks about the Assam
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took, I recall that we define horizontal ass and
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tits as the limit and six persons infinity of a
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certain function. So technically, here we have proven
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that why equal zero is a horizontal as him total
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dysfunction on. So, by looking at the ground
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, we identify the horizontal awesome totals the X axis
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and we see that this function crosses thie XX is
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an infinite amount of time. Many, many times
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are oscillating up and down over the X axis,
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and the function approaches zero as expressions infinity but isn't
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exactly equal to zero. So the answers and an
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infinite amount of times.