Use continuity to evaluate the limit. lim x→16 20 + x 20 + x step 1 consider the intervals for which the numerator and the denominator are continuous. the numerator 20 + x is continuous on the interval the denominator 20 + x is continuous and nonzero on the interval

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Answer:

[tex]\lim_{x \to 16} \frac{20+x}{20+x}[/tex] = 1

Step-by-step explanation:

We are given the expression, [tex]\lim_{x \to 16} \frac{20+x}{20+x}[/tex].

Since, we have that,

The numerator and denominator is (20+x), which is a polynomial is continuous for all the real numbers i.e. for all x belonging to [tex](-\infty,\infty)[/tex].

Thus, the limit exists and is given by,

[tex]\lim_{x \to 16} \frac{20+x}{20+x}[/tex] = [tex]\frac{20+16}{20+16}[/tex] = [tex]\frac{36}{36}[/tex] = 1.

So, [tex]\lim_{x \to 16} \frac{20+x}{20+x}[/tex] = 1.

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