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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 = √(1 2 +(-3) 2 ) [I would explain w...
OG
Answered by Odin G. • Maths tutor
10463 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) - (integral) 1= xln(x) -x + C
SR
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 = x 2 +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 (minimum point) is (-3/2,-1/...
RI
Answered by Ross I. • Maths tutor
3639 Views

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

x 2 +3x+2 = (x+p) 2 +q (x+3/2) 2 = x 2 +3x+9/4 x 2 +3x+2 = (x+3/2) 2 -9/4+2 x 2 +3x+2 = (x+3/2) 2 -1/4
RI
Answered by Ross I. • Maths tutor
8412 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 differentiate you f...
HM
Answered by Hannah M. • Maths tutor
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