Let i cr be an interval and f, 9: 1 + r be differentiable functions at cei. by caratheodory's theorem there exist functions 6,0: 1 + r which are continuous at c, with 6 (c) = f'(c) and 4 (c) = g' (c) such that for all xe i we have f (x) = f (c) + 6(x) (x – c), g(x) = g(e) + (l) (x – c) use this criteria to prove: 1. the product rule of differentiation; 2. the differentiation formula for inverse functions.

here you hope this .

step-by-step explanation:

hypotenuse = √(15² + 8²)

=  √(225 +64)

=  √(289) = 17

sin(x) = cos(y) = 8/17

they are identical so long as you are doing the sine of one angle and the cosine of the only other angle that isn't the right angle.

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation:

3, 12, 48, 384, 1536, 6144, 24576, 98304

step-by-step explanation:

just keep timing it by 4.

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step-by-step explanation: