2 years ago

How to solve integral of sec x ?

Mathematics

1 answer:

Alexandra [31]2 years ago

4 0

The formula is:

$\int\limits \, sec (x)dx = ln | tan(x) + sec(x) | + C$

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Consider the following function. f(x) = 9 − x2/3 Find f(−27) and f(27). f(−27) = f(27) = Find all values c in (−27, 27) such tha

oksano4ka [1.4K]

I guess the function is $f(x)=9-x^{2/3}$ . Then $f(-27)=0$ and $f(27)=0$ .

The derivative is $f'(x)=-\dfrac23 x^{-1/3}$ , but there is no $c$ such that

$-\dfrac23c^{-1/3}=0$

This doesn't contradict Rolle's theorem because $f'(0)$ does not exists. In other words, $f$ is not differentiable on (-27, 27), so the conditions of Rolle's theorem are not met. (Looks like that would be the last option, or the second to last option if the last one is "Nothing can be concluded")