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Let f(x)=xln(x)-x. Find f'(x). Hence or otherwise, evaluate the integral of ln(x^3) between 1 and e.

We use the product rule with u=x and v=ln(x) (so u'=1 andv'=1/x) to differentiate xln(x) to ln(x)+1, and -x just differentiates to -1, hence we have. f'(x)=ln(x). Now note that ln(x^3)=3ln(x) using propertie...
MJ
Answered by Matthew J. • Maths tutor
4014 Views

Solve the simultaneous equations: 3x-y=1, x^2+y^2=5

x=1, y=2 x=-2/5, y=-11/5
CW
Answered by Chloe W. • Maths tutor
4476 Views

Work out the value of the following:

36 1/2 = 6(The square root of 36 is 6) 2) 23 0 = 1(Anything to the power of 0 is 1) 3) 27 -2/3 = 3 -2 = 1/3 2 = 1/9
HA
Answered by Hafsah A. • Maths tutor
3432 Views

How do you find a missing side length in a right-angled triangle?

Use Pythagoras' theorem. a 2 + b 2 = c 2 . The longest side of the triangle is the hypotenuse, and it is the side opposite the right angle. We use the length of this side as 'c' if we have it. 'a' and 'b' ar...
JD
Answered by James D. • Maths tutor
13282 Views

Draw the line X+Y=3 on the graph from x = -3 to x = 3

The easiest way is probably to write a table with all of the X and Y values. Write out all of the x values and substitute them into the formula to see what value of Y you need to get the value of 3.X Y-3 6-2...
MN
4149 Views