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What is the sum of the geometric series 1 + 1/3 + 1/9 + 1/27 ...

The geometric series takes the form of ax^n where n is a number from 0 to infinity with 0 being the first number in the series.

The sum of this series is S = a + ax + ax^2 + ...

If we brea...

Answered by Ryan T. • Maths tutor

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Integrate (3x^2-x^3)dx

With integration like this, you can look at each appearance of x individually. Firstly there is a rule to follow that is the power of X in each case increases by 1 and then that increase power divides th...

Answered by Josh T. • Maths tutor

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x = t^3 + t, y = t^2 +1, find dy/dx

dy/dx = dy/dt x dt/dx

x = t³ + t

dx/dt = 3t² +1

y = t² +1

dy/dt = 2t

dy/dx = 2t x (1 / (3t² +1) )

= 2t / (3t²

Answered by Sukhwinder K. • Maths tutor

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Express 5cosx - 3sinx in the form Rcos(x+a).

cos(x+a)=cosxcosa-sinxsina so cosa=5 sina=3 which means tana=3/5 a=0.54 RADIANS R=sqrt(5²+3²). =sqrt(34) so sqrt(34)cos(x+0.54)

Answered by Elizabeth H. • Maths tutor

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Differentiate sin(5x) and 3cos(x) and 3tan(5x)

sin cos -sin -cos (down is differentiate and up is integrate) so, y = sin5x dy/dx = 5cos5x y=3cox dy/dx = -3sinx y=3tan5x dy/dx = 15sec²(5x) (remember sec(x) is the reciprocal of cos(...

Answered by Abi C. • Maths tutor

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