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When using the trapezium rule to approximate area underneath a curve between 2 limits, what is the effect of increasing the number of strips used?

Ideally to find the exact area under the curve, we would integrate the function and substitute in the bounds given. However, using the trapezium rule gives an approximation whereby using more trapezia increa...
MM
Answered by Manan M. • Maths tutor
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Prove that sin(x)+sin(y)=2sin((x+y)/2)cos((x-y)/2)

We know that 1. sin(a+b) = sin(a)cos(b)+sin(b)cos(a) and 2. sin(a-b) = sin(a)cos(b)-sin(b)cos(a) Add equations 1. and 2. sin(a+b)+sin(a-b) = 2sin(a)cos(b)+sin(b)cos(a)-sin(b)cos(a) = 2sin(a)cos(b) Let x=a+b ...
AV
Answered by Anna V. • Maths tutor
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The points A and B have coordinates (3, 4) and (7, 6) respectively. The straight line l passes through A and is perpendicular to AB. Find an equation for l, giving your answer in the form ax + by + c = 0, where a, b and c are integers.

For the line passing through A and B: m = (y2-y1)/(x2-x1) = (-6-4)/(7-3) = -5/2 For the perpendicular line: m = -1/(-5/2) = 2/5 y - y1 = m*(x - x1) >> y - 4 = (2/5)*(x - 3) >> 5y - 20 = 2x - 6 &g...
DA
Answered by Deji A. • Maths tutor
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Find the gradient of the tangent to the curve with the equation y = (3x^4 - 18)/x at the point where x = 3

y = (3x 4 - 18)/x The gradient of a tangent to a curve is equal to dy/dx However, we must simplify this equation before we can differentiate it; y = 3x 3 - 18/x = 3x 3 - 18x -1 dy/dx = 3(3x 2 ) - (-1)(18x -2...
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Answered by Rachel O. • Maths tutor
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Find the turning points of the curve y = x^3 +5x^2 -6x +4

y = x 3 +5 x 2 -6 x +4 dy/dx = 3 x 2 +10 x -6 at turning points dy/dx = 0 therefore 3 x 2 +10 x -6 = 0 This quadratic is factorisable. When factorised you get: (3 x -2)( x +4) = 0 therefore x = 2/3 and -4 at...
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Answered by Arshan B. • Maths tutor
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