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How to find the equation of a tangent to a curve at a specific point.

The first thing to remember is that the tangent to the curve at a given point has the same gradient as the curve at that point. Let's consider the general case y=f(x) at a point c=(x1,y1). Step 1:We have to ...
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Answered by Rafe L. • Maths tutor
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Integrating cos^2(x)+5sin^2(x)

Firstly, note that cos^2(x)+5sin^2(x)= cos^2(x) +sin^2(x) +4sin^2(x). By trignoemtric identies, cos^2(x)+sin^2(x)=1 and so we can just integrate 1+4sin^2(x) since this is equal to cos^2(x)+5sin^2(x). Again, ...
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Answered by Rafe L. • Maths tutor
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Find the all the angles of a triangle with side lengths of 8cm, 11cm and 11cm.

Using the knowledge of a 2 = b 2 + c 2 - 2bcCos(A) Rearrange to aquire Cos(A) = (b 2 + c 2 - a 2 )/2bc Then input the values to obtain the angles of 42, 69, 69.
AJ
Answered by Alexander J. • Maths tutor
5853 Views

Differentiate with respect to x: 4(x^3) + 2x

d/dx(4x 3 + 2x) = d/dx (4x 3 ) + d/dx(2x) = 4(3x 2 ) + x = 12x 2 + x
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Answered by Alexander J. • Maths tutor
5494 Views

How do I add up the integers from 1 to 1000 without going insane?

Suppose you are asked by your teacher to sum all the integers from 1 up to 1000. You might be thinking they must hold some kind of grudge against you. If you try to calculate the sum by adding on each intege...
MB
Answered by Matthew B. • Maths tutor
7455 Views