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What are the different steps involved in Proof by Induction?

The first step is to prove that the result is true for n=1.The second step is to assume that the result is true for n=k where k is any positive integer.The third step is to prove that the results is true ...

Answered by Álvaro F. Maths tutor
2915 Views

For the curve, y = e^(3x) - 6e^(2x) + 32 ,find the exact x-coordinate of the minimum point and verify that the y-coordinate of the minimum point is 0.

At the minimum point, the gradient will be zero, so we differentiate the equation, giving us dy/dx = 3e3x - 12e2x. If the gradient is zero at the minimum point, we can set dy/dx = 0,...

Answered by Matthew A. Maths tutor
6581 Views

Find the unknown side A ( trigonometry with one known side and an angle)

  1. First we need to make sure we have a nicely labelled triangle, identifying which sides are the adjacent, opposite and hypotenuse. 2) Once these are labelled we will can work out which trig function ...
Answered by Tobias L. Maths tutor
2701 Views

Find the equation of the tangent to y = 2x^2 + 7 at x = 3.

The first step here is to identify what to do. Differentiating the equation y = 2x^2 + 7 will result in dy/dx = 4x. Given that you know that x = 3, you can substitute x = 3 into 4x which gives you 4(3) = ...

Answered by Danielle C. Maths tutor
3107 Views

(https://qualifications.pearson.com/content/dam/pdf/A-Level/Mathematics/2013/Exam-materials/6666_01_que_20160624.pdf) Question 6.(i)

First split up the fraction into partial fractions as this is more easily integrated. It can be seen that the denominator has factors y and (3y+2), therefore we can say the original fraction is equal to p...

Answered by Tom J. Maths tutor
3219 Views

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