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A trillion is 10^12. Which of the following is bigger: the three trillionth root of 3 or the two trillionth root of 2? You may assume that if 0 < x < y, then 0 < x^n < y^n for integer values of n greater than or equal to 1.

For this sort of question, the easiest approach is to make an educated guess at the correct answer, and prove that this must be correct by contradiction. As taking the root of something has a large effect...

Answered by Benjamin C. • MAT tutor

1483 Views

Let E be an ellipse with equation (x/3)^2 + (y/4)^2 = 1. Find the equation of the tangent to E at the point P where x = √3 and y > 0, in the form ax + by = c, where a, b and c are rational.

In order to find the equation of the tangent to a curve at a point (x₁, y₁), we use the equation y - y₁ = m(x - x₁), where m is the gradient of the curve at (x<...

Answered by Benjamin C. • Further Mathematics tutor

2368 Views

log8(5) = b. Express log4(10) in terms of b

log₈5=b

using the base change rule

log₈5=log₄5/log₄8

log₄8 can be solved:...

Answered by Beatrice M. • Maths tutor

9967 Views

Let f(x) = x * sin(2x). Find the area beneath the graph of y = f(x), bounded by the x-axis, the y-axis and the line x = π/2.

After short consideration, we see that we must integrate f(x) with respect to x, between 0 and π/2, using integration by parts. Taking the formula for integration by parts, we set u = x and dv/dx = sin(2x...

Answered by Benjamin C. • Maths tutor

4431 Views

Is there a difference between Law and Morality?

This question points to the clash between legal positivism and natural law theory. It can be interpreted in two different ways. The first interpretation would consider whether there is a requirement that ...

Answered by Mohamed S. • LNAT tutor

4946 Views