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Maths
A Level

Integrate 2x/[(x+1)(2x-4)

2x/[(x+1)(2x-4)] = [A/(x+1) + B/(2x-4)]x = A(x-2) + B(x+1)x = -1-1 = A(-3)A = 1/3x = 2 2 = B(3)B = 2/3 therefore.... 2x/[(x+1)(2x-4)] ...

Answered by Lukas A. Maths tutor
3823 Views

Prove that 1+2+...+n = n(n+1)/2 for all integers n>0. (Hint: Use induction.)

Let us procede by induction:

First case: n=1. Then LHS (left hand side) = 1 and RHS (right hand side) = 1(1+1)/2 = 1. Therefore, we see that the statement is true for n=1.

Now, we carry out ...

Answered by Aran T. Maths tutor
3761 Views

Given that x = ln(sec(2y)) find dy/dx

x = ln (sec (2y))

The chain rule states that d/dy f (g (y)) = f'(g(y)). g'(y)

Here g(y) = sec(2y) so g'(y) = 2.sec(2y).tan(2y)

And f(y) = ln (y) so f'(y) = 1 / y

Thus dx/dy = (...

Answered by Dom H. Maths tutor
11558 Views

f(x) = x^3 + 3x^2 + 5. Find f''(x)

f''(x) means that we need to differentiate the function f(x) twice (f'(x) would mean we need to do it once). Differentiation means we multiply the coefficient by the power, and subtract one from the power...

Answered by Felix M. Maths tutor
3355 Views

The line l1 has equation y = −2x + 3. The line l2 is perpendicular to l1 and passes through the point (5, 6). (a) Find an equation for l2 in the form ax + by + c = 0, where a, b and c are integers.

The first thing to look at is l2 and l1 being perpendicular. This means the gradients of the two lines multiplied together = -1 . To determine the gradient a student could differentiate l1 but a slightly ...

Answered by Roman Paul M. Maths tutor
15564 Views

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