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Solve the equation 5^x = 8, giving your answer to 3 significant figures.

Since there is an x written as a power here, it suggests that this question should be solved using logs (here assume I am using the natural logarithm, which has base e). Taking logs of both sides of the equa...
HM
Answered by Hannah M. • Maths tutor
23298 Views

Prove that 1/(tanx) + tanx = 1/sinxcosx

The key here is to realise that tanx = sinx/cosx. If we write out the left hand side of the equation in terms of sine and cosine we get: cosx/sinx + sinx/cosx These two fractions can be put over a common den...
HM
Answered by Hannah M. • Maths tutor
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Find the inverse of y = (5x-4) / (2x+3)

the aim of finsing the inverse is making x the subject. To start we need to multiply both sides by: (2x+3), giving us: y(2x+3) = 5x-4 now we need to expand the brackets: 2xy +3y = 5x-4 now gather all the x c...
XA
Answered by Xuanyi A. • Maths tutor
6354 Views

How do you integrate by parts?

To integrate the product of two functions - say f(x) = xsinx, the product of g(x) = x and h(x) = sin(x) - the we use integration by parts. Since integration is the inverse of differentiation, we'll appeal to...
PK
Answered by Patrick K. • Maths tutor
6729 Views

Given that (2x + 11 )/(2x + 1)(x + 3) ≡ A /(2x + 1) + B /(x + 3) , find the values of the constants A and B. Hence show that the integral from 0 to 2 (2x + 11)/ (2x + 1)(x + 3) dx = ln 15.

First starting from the right hand side. A /(2x + 1) + B /(x + 3) = A(x+3)+B(2x+1)/(x+3)(2x+1) Therefore the numerator = (A+2B)x+(3A+B) Equating this numorator with the Left hand side we are presented with t...
GD
Answered by George D. • Maths tutor
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