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A curve has equation x = (y+5)ln(2y-7); (i) Find dx/dy in terms of y; (ii) Find the gradient of the curve where it crosses the y-axis.

(i) To find the derivative we will use the product rule. Let u = y+5 and v=ln(2y-7). Then dx/dy = du/dy v + u dv/dy = ln(2y-7) + (y+5)*2/2y-7 (used the chain rule in 2nd term - can explain this on white boar...
SP
Answered by Szymon P. • Maths tutor
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Solve the equation: log5 (4x+3)−log5 (x−1)=2.

As both terms on the left hand side have base 5 we know we can combine them. When dealing with logs, a minus means we can divide them, and a plus means we can multiply them. This will leave us with log5(4x+3...
HG
Answered by Hugh G. • Maths tutor
9753 Views

Show that 1+cot^2(x)=cosec^2(x)

Need to remember that:sin 2 (x)+cos 2 (x)=1 (eq.1)Divide the whole eq.1 by sin 2 (x)to get:sin 2 (x)/sin 2 x+cos 2 (x)/sin 2 (x)=1 /sin 2 x Which is the same as:1+cot 2 x=cosec 2 x
TD
Answered by Tutor114151 D. • Maths tutor
62303 Views

Find the stationary point(s) of the curve: y = 3x^4 - 8x^3 - 3.

Firstly. Recognise which method you should use to approach this question. In this case, you can find the stationary point of a curve where its gradient is 0 i.e. at a point where the gradient changes from po...
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Answered by Laurene L. • Maths tutor
5575 Views

OCR C2 2015 Question 8: (a) Use logarithms to solve the equation 2^(n-3) = 18,000 , giving your answer correct to 3 significant figures. (b) Solve the simultaneous equations log2(x) + log2(y) = 8 & log2(x^2/y) = 7.

(a) This question actually tells us what to do . It is very hard to miss " use logarithms to solve... ". So our first step is going to be to use logs (especially as we can also see that is very lit...
JH
Answered by Jonathan H. • Maths tutor
8082 Views