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The volume of liquid in a container is given by v=(3h^2+4)^(3/2)-8, find dV/dh when h = 0.6

Chain rule: dV/dh=9h(3h^2+4)^(1/2)
sub in h=0.6 , dV/dh = 12.17

Answered by Johnny H. • Maths tutor

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Given that y=(4x^2)lnx, find f"(x) when x=e^2

Product rule: first order derivative = 8xlnx+4x Second order derivative = 8lnx+12 Sub in e^2 , 16lne + 12 = 24

Answered by Johnny H. • Maths tutor

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Textbooks are stored on 2 shelves. Each shelf is 0.72m long and each textbook is 30mm wide. Can 50 textbooks be stored on these 2 shelves?

First off, we better convert the 30mm into m. Now, we know that in 1cm there are 10mm. So in 2cm, there are going to 20mm and in 3cm there are going to be 30mm. So each textbook is really 3cm thick. Now, ...

Answered by Jack D. • Maths tutor

9246 Views

What is the difference between differentiation and integration, and why do we need Calculus at all?

We need calculus to find out the properties complex curves that we cannot find with simple arithmetic as we would with linear graphs. Differentiation allows us to calculate the gradient of a curve at a sp...

Answered by Samuel H. • Maths tutor

10333 Views

The equation (t – 1)x^2 + 4x + (t – 5) = 0, where t is a constant has no real roots. Show that t satisfies t2–6t+1>0

This is a quadratic equation of the form ax^2 + bx +c, where (t-1)=a 4=b . (t-5)=0 Therefore if there are no real roots, you get that b^2-4ac<0. (using the quadratic formula)

First plug in valu...

Answered by Rachel Y. • Maths tutor

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