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Integrate 3x^2

3x^2 Integrate you add one to the power and divide by that number. In this case:3x^2 = (3x^3)/3 = x^3

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Explain how one of Gettier's original counter examples attacks the tripartite view of knowledge

The tripartite view of knowledge defines propositional knowledge as justified true belief. Edmund Gettier famously contested this definition by providing a series of counter examples which show that there...

Answered by Sammy M. • Philosophy tutor

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The function f has domain (-∞, 0) and is defines as f(x) = (x^2 + 2)/(x^2 + 5) (here ^ is used to represent a power). Show that f'(x) < 0. What is the range of f?

First notice that f(x) = u/v. So f'(x) =[ v(u') - u(v')]/v² (the Quotient rule). After working it out, we find f'(x) = 6x/(x²+ 5)²(the steps can be shown on the whiteboa...

Answered by Chris C. • Maths tutor

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Given that y = (1 + 3x^2)^(1/3) , use the chain rule to find dy/dx in terms of x.

Take u = 1+3x² , this gives that y = u^1/3. By the chain rule we have that dy/dx = dy/du * du/dx. By differentiating y = u^1/3 with respect to u giv...

Answered by Jasmine S. • Maths tutor

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What are electrophilic addition reactions of alkenes?

Alkenes contain a pi bond, which is a site of high electron density, since it contains a pair of electrons delocalised around the two bonded carbon atoms. Because of this, the pi bond can act as a nucleop...

Answered by Jessica M. • Chemistry tutor

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