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How do you solve the equation e^2x - 2e^x - 3 = 0 ?

This is a 'quadratic in e^x'. The easiest way to recognise this when starting problems like this is to let y=e^x. As you practice problems like this, you will find yourself moving away from this step. But it...
LC
Answered by Lewis C. • Maths tutor
15871 Views

How do you simplify something of the form Acos(x) + Bsin(x) ?

This sort of question is quite common, and a little bit complicated, so the explanation is quite long! But it's a great one to understand. There are a few tricks you need to know to be able to do it. The fir...
JM
Answered by Jack M. • Maths tutor
15745 Views

f(x) = (4x + 1)/(x - 2) with x > 2. Find a value for 'x' such that f'(x) (first derivative of f(x) with respect to x) is equal to -1.

Re-write f(x) using indicies, so that the use of the product rule becomes more clear => f(x) = (4x + 1) *(x - 2)^-1 where ^ means 'raised to the power of' and * means 'multiplied by'. use the product rule...
ZS
Answered by Zak S. • Maths tutor
5228 Views

Find the exact solutions for 4 − x^2 = |2x − 1|

x=-1 x=-1+6 0.5
SV
Answered by Shroya V. • Maths tutor
6183 Views

What is a confidence interval?

Using the normal distribution, we can estimate a range of values which we expect to contain the mean. For example, if we take a sample of 30 students height, we can estimate the mean height of students in th...
AR
Answered by Alexander R. • Maths tutor
4833 Views