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How come x^2 = 25 has 2 solutions but x=root(25) only has one? Aren't they the same thing?

(This is something that I didnt fully understand for quite a while at school.) So when we are solving x²=25, in order to get x "on it's own" we square root both sides. However the def...

Answered by Dylan J. • Maths tutor

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How would I find a the tangent of a point on a line?

You will end up with an equation with the form y = mx + c you should be familiar with from GCSE First you would need to differentiate the equation of the line For example if you had f(x) = x³+...

Answered by Simon G. • Maths tutor

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Find the equation of the tangent to the curve y = 3x^2(x+2)^6 at the point (-1,3), in the form y = mx+c

Curve: y = 3x²(x+2)⁶Coordinate: (-1, 3)

This is typically a C3/4 level question because of the differentiation, but the rest of t...

Answered by BUNEME K. • Maths tutor

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Integrate sin(x)cos(x)^2 from 0 to π/2

Use substitution u=cos(x) resulting in du=-sin(x)dx: ∫₀^π/2sin(x)cos(x)^2dx = ∫₀^π/2-u^2du = [-1/3 u^3]_x=0^x=π/2 = [-1/3 cos(x)^3]₀

Answered by Benedek S. • Maths tutor

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If y = exp(x^2), find dy/dx

Recall that the derivative of exp(x) is exp(x), but notice this question is slightly more complex due to the x^2 term. This is example of differentiationg composite functions, and so the chain rule is req...

Answered by Stuart B. • Maths tutor

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