3 years ago

Is the following statement TRUE or FALSE? Select the best choice from the following to justify your

Mathematics

1 answer:

ale4655 [162]3 years ago

5 0

Answer:

$first \: answer \: is \: true$

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Lim x->pi/3 ((2cosx-1)/(tan^2x-3))

beks73 [17]

You can check that the limit comes in an undefined form:

$\displaystyle \lim_{x\to\frac{\pi}{3}} \frac{2\cos(x)-1}{\tan^2(x)-3}=\dfrac{0}{0}$

In these cases, we can use de l'Hospital rule, and evaluate the limit of the ratio of the derivatives. We have:

$\dfrac{\text{d}}{\text{d}x}2\cos(x)-1 = -2\sin(x)$

and

$\dfrac{\text{d}}{\text{d}x}\tan^2(x)-3 = 2\dfrac{\tan(x)}{\cos^2(x)}=\dfrac{2\sin(x)}{\cos^3(x)}$

So, we have

$\displaystyle \lim_{x\to\frac{\pi}{3}} \frac{2\cos(x)-1}{\tan^2(x)-3}=\lim_{x\to\frac{\pi}{3}} \dfrac{-2\sin(x)}{\frac{2\sin(x)}{\cos^3(x)}}=\lim_{x\to\frac{\pi}{3}}-\cos^3(x)=-\cos^3\left(\dfrac{\pi}{3}\right)$

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3 years ago

What is the greatest common factor of the terms in the expression 21x-18x+28xy?

natulia [17]

The answer i got was c because the letter x goes into each of them because they each have a x in them. It would be B but 3 doesnt go into 28.

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The number 42 is composite or prime.

iren [92.7K]

Answer:

Composite

Step-by-step explanation:

Composite means having more than 2 factors

1, 42, 2, 21, 6, 7 are the factors therefore, it is composite

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