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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

2291 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

9835 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

4321 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

4899 Views

How do I conjugate regular verbs in the present tense?

There are 3 types of regular verb in French; verbs ending in -er, verbs ending in -ir, and verbs ending in -re. They each have their own...

Answered by Isabelle W. • French tutor

2622 Views