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Solve the ODE y' = -x/y.

we have dy/dx = -x/y , so we treat the differentials as fractions and write y dy = -x dx. Now integrating the left side with respect to y and the right side with respect to x, we have y 2 /2 = -x 2 /2 + C. W...
JM
3817 Views

How do I multiply and divide indices?

First you need to understand what an index (or power) is. It’s just a compact way of writing a number multiplied by itself a number of times. For example: 3 4 = 3x3x3x3 and a 2 = axa. If two indices have the...
SM
Answered by Sarah M. • Maths tutor
14380 Views

I've been told that I can't, in general, differentiate functions involving absolute values (e.g. f(x) = |x|). Why is that?

When you differentiate a function which has only one parameter, like f(x), you are finding a new function, f'(x), which gives the gradient of your original function at every point. You'll probably remember t...
RW
Answered by Richard W. • Maths tutor
3582 Views

What are the solutions of (x^3)+6 = 2(x^2)+5x given x = 3 is a solution?

Firstly we will put this into a form equal to zero, by rearranging to get x 3 -2x 2 -5x+6 = 0. This is because in order to solve a polynomial we first need to set it equal to zero. We now know that the value...
WB
Answered by William B. • Maths tutor
6896 Views

When using the trapezium rule to approximate area underneath a curve between 2 limits, what is the effect of increasing the number of strips used?

Ideally to find the exact area under the curve, we would integrate the function and substitute in the bounds given. However, using the trapezium rule gives an approximation whereby using more trapezia increa...
MM
Answered by Manan M. • Maths tutor
10351 Views