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4 years ago

14

Geroge bought 4 submarine sandwiches for a birthday party. if each person eats 2/3 of a sandwich, how many people can Geroge fee

d?

1 answer:

Vlada [557]4 years ago

7 0

George can feed up to 6 people because there are 12 pieces of sandwich and each person eats 2

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Why do you need to find the number that is halfway between 0 and 1 and 1/2 ?

labwork [276]

Answer:

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3 years ago

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

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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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