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use the substitution u=2+ln(x) to show that int(e,1(ln(x)/x(2+ln(x)^2))dx)=p+ln(q) , where p and q are rational numbers.

So u=2+lnx, therefore du/dx=1/x , we can work out the new upper and new lower limit by substitute in e and 1 into 2+lnx , and we get 2+ln(e)=3 , 2+ln(1)=2Rearrange the differential we get dx=xdu , substit...

Answered by • Maths tutor

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Solve the quadratic inequality: x^2 - 5x + 4 < 0

x²-5x+4 <0First we ignore the inequality and try to solve the equation x²-5x+4=0, which we do via factorising (x-4)(x-1)=0. x = 4 or x=1We draw the graph using our solution, going...

Answered by Hariz H. • Maths tutor

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What is the electron figuration of a copper ion? The n what is the electron configuration of a copper2+ ion

The electron configuration is:{Ar]4s13d10Copper donates one of the electrons in its S orbital to the d orbital in order to make itself more stableCopper 2+ is [Ar]3d9The 4s electrons are lost first as the...

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Why does a rise in interest rates lead to a fall in inflation?

A rise in interest rates increases the cost of borrowing and increases the reward for saving. This means that there is a double effect, people are disincentivised to borrow money and spend it, as well as ...

Answered by Karan S. • Economics tutor

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Find two positive numbers whose sum is 100 and whose product is a maximum.

Call the two numbers x and y. The constraint is that x + y =100, and we need to maximise A=xy.
Rearrange the constraint to y = 100 - x, and substitute into the product equation.
A = x(100-x) = ...

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