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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 x 2 =25, in order to get x "on it's own" we square root both sides. However the definition of r...
DJ
Answered by Dylan J. • Maths tutor
8991 Views

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) = x 3 + 2x and the c...
SG
Answered by Simon G. • Maths tutor
3527 Views

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 = 3x 2 (x+2) 6 Coordinate: (-1, 3) This is typically a C3/4 level question because of the differentiation, but the rest of the question is possible with year 12 maths knowledge. The best way to tack...
BK
Answered by BUNEME K. • Maths tutor
12705 Views

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

Use substitution u=cos(x) resulting in du=-sin(x)dx: ∫ 0 π/2 sin(x)cos(x)^2dx = ∫ 0 π/2 -u^2du = [-1/3 u^3] x=0 x=π/2 = [-1/3 cos(x)^3] 0 π/2 = (-1/3 cos(π/2)^3) - (-1/3 cos(0)^3) = (-1/3 0^3 ) - (-1/3 1^3) ...
BS
Answered by Benedek S. • Maths tutor
9587 Views

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 requir...
SB
Answered by Stuart B. • Maths tutor
8515 Views