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Write cosx - 3sinx in the form Rcos(x + a)

Rcos(x + a) = Rcosxcosa - Rsinxsina
By comparing cosx - 3sinx to the new expression, we can see that:
Rsina = 3 and Rcosa = 1
If we square both and add them, we can see R = √(1²

Answered by Odin G. • Maths tutor

9785 Views

A) Differentiate ln(x) b) integrate ln(x)

A) y=ln(x) E^y = x E^y(dy/dx ) = 1 E^ln(x)(dy/dx) = 1 X(dy/dx) = 1 Dy/dx = 1/xb) y = 1 * ln(x) V = ln(x) U= x dv/dx =1/x Du/dx = 1xln(x) - (integral) x * (1/x)xln(x) - (integ...

Answered by Stanley R. • Maths tutor

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(Follow on from previous question) A curve has equation y= x^2+3x+2. Use your previous results to i) find the vertex of the curve ii) find the equation of the line of symmetry of the curve

i) y = x²+3x+2 = (x+3/2)²-1/4Solution for (x+3/2) = 0 is x coordinate, which is x = -3/2Solution for y value is the additional constant, which is y = -1/4Therefore the vertex (minimu...

Answered by Ross I. • Maths tutor

3325 Views

Express x^2+3x+2 in the form (x+p)^2+q, where p and q are rational numbers.

x²+3x+2 = (x+p)²+q (x+3/2)² = x²+3x+9/4 x²+3x+2 = (x+3/2)²-9/4+2 x²+3x+2 = (x+3/2)²-1/4

Answered by Ross I. • Maths tutor

8003 Views

How can I remember how to differentiate and integrate cos and sin?

I find it is best whenever you open your maths paper to draw this diagram to help you remember: Sin(X) -> cos(X)-> -sin(X) -> -cos(X)----->
{Drawn in a circle on the board}
To diff...

Answered by Hannah M. • Maths tutor

6128 Views