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Find the equation of the tangent to the curve y = 2 ln(2e - x) at the point on the curve where x = e.

The first step is to find the y coordinate at the point on the curve where x = e. To do this we subsitute x = e into the equation of the curve, so y = 2ln(2e - x) becomes y = 2ln(2e - e). Simplifying t...

Answered by Rhiannon T. • Maths tutor

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Solve x^2 - 6x - 2=0 giving your answer in simplified surd form.

SInce the question requires simplified surd form, it makes sense to use the quadratic formula immediately for this question.

This would give us

x = 6 [+-] squareroot(36-(4x1...

Answered by Molly B. • Maths tutor

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Use logarithms to solve 9^x=15

According to the rules of logarithms, when you take a log of something to the power of something, you multiply the log of the base by the power, so in this case, taking logs of both sides would give us...

Answered by Molly B. • Maths tutor

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Integrate the following function by parts and reduce it to it's simplest form. f(x) = ln(x).

First note that ln(x) = 1ln(x), this is in the form udv/dx.

Let dv/dx = 1 and u = ln(x).

du/dx = 1/x from the standard results and v = x by integration.

Answered by Ryan B. • Maths tutor

4665 Views

Integrate sinx*ln(cosx) with respect to x.

1. ʃ sinx*ln(cosx) dx

First notice the composition ln(cosx). To make the expression easier to integrate we try substitution (substitution is often useful when trying to integrate expressi...

Answered by Darshan S. • Maths tutor

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