2 years ago

10. What is the missing statement in the proof?

1 answer:

7 0

Answer:

∠3 ≅ ∠2.

Step-by-step explanation:

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sineoko [7]

I'm assuming the limit is supposed to be

$\displaystyle\lim_{x\to3}\frac{\sqrt{2x+3}-\sqrt{3x}}{x^2-3x}$

Multiply the numerator by its conjugate, and do the same with the denominator:

$\left(\sqrt{2x+3}-\sqrt{3x}\right)\left(\sqrt{2x+3}+\sqrt{3x}\right)=\left(\sqrt{2x+3}\right)^2-\left(\sqrt{3x}\right)^2=-(x-3)$

so that in the limit, we have

$\displaystyle\lim_{x\to3}\frac{-(x-3)}{(x^2-3x)\left(\sqrt{2x+3}+\sqrt{3x}\right)}$

Factorize the first term in the denominator as

$x^2-3x=x(x-3)$

The $x-3$ terms cancel, leaving you with

$\displaystyle\lim_{x\to3}\frac{-1}{x\left(\sqrt{2x+3}+\sqrt{3x}\right)}$

and the limand is continuous at $x=3$ , so we can substitute it to find the limit has a value of -1/18.

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deff fn [24]

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spin [16.1K]

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Len [333]

The answer is k=160..............

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AVprozaik [17]

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