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bogdanovich [222]
3 years ago
8

Intervals, extrema and behaviot

Mathematics
1 answer:
Pani-rosa [81]3 years ago
4 0

9514 1404 393

Answer:

  (a)  1

Step-by-step explanation:

For large variable magnitude, the value of a rational function approaches the ratio of the highest-degree terms of the numerator and denominator*. Here, that is ...

  x/x = 1

f(x) approaches 1 as x approaches infinity.

__

* The function approaches the line or curve defined by the quotient. (The remainder is ignored in this case.) Here, f(x) = 1 + 3/(x-3), so the quotient is the constant 1.

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Step-by-step explanation:

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yawa3891 [41]

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8 0
3 years ago
Someone can help?? ​
oee [108]

Answer:

Step-by-step explanation:

let  cos^{-1}x=t

cos t=x

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\lim_{x \to 1} \frac{1-\sqrt{x}}{(cos ^{-1}x)^2 } \\= \lim_{t \to 0} \frac{1-\sqrt{cos~t}}{t^2} \times \frac{1+\sqrt{cos~t}}{1+\sqrt{cos ~t}} \\= \lim_{t \to 0} \frac{1-cos~t}{t^2(1+\sqrt{cos~t})}}  \\= \lim_{t \to 0 }\frac{2 sin^2~\frac{t}{2}}{t^2(1+\sqrt{cos~t})}} \\= 2\lim_{t \to 0 }(\frac{sin~t/2}{\frac{t}{2} })^2 \times \frac{1}{4} \times  \lim_{t \to 0 }\frac{1}{1+\sqrt{cos~t}} \\=\frac{2}4} \times 1^2 \times \frac{1}{1+\sqrt{cos~0}} \\=\frac{1}{2} \times \frac{1}{1+1} \\=\frac{1}{4}

4 0
3 years ago
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