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y = 4x/(x^2+5). a) Find dy/dx, writing your answer as a single fraction in its simplest form. b) Hence find the set of values of x for which dy/dx < 0

a) We need to differentiate this equation using the quotient rule (Given that it is a fraction with an x term on both the top and bottom of the fraction). We assign the numerator and denominator as follows: ...
JF
Answered by James F. • Maths tutor
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A curve has parametric equations: x=(t-1)^3 and y= 3t - 8/(t^2). Find dy/dx in terms of t. Then find the equation of the normal at the point on the curve where t=2.

dx/dt = 3(t-1) 2 dy/dt = 3 + 16t -3 dy/dx=(dy/dt)(dt/dx) dy/dx = 3 + 16t -3 / 3(t-1) 2 At t=2 dy/dx= (3 + 16/8) / 3 = 5/3 Gradient of the normal = -3/5with t=2 y-4=0x-1=0 y=mx + c y - 4 = -3/5(x-1) 3x +5y -2...
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Answered by Jasmin H. • Maths tutor
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How can functions be transformed?

A function, y = f(x), with y on the vertical axis and x on the horizontal axis, can be transformed by 3 different ways: It can be stretched (or shrunk)If y = f(ax), the function is stretched by a scale facto...
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Answered by Jack M. • Maths tutor
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The second and fifth terms of a geometric series are 750 and -6 respectively. Find: (1) the common ratio; (2) the first term of the series; (3) the sum to infinity of the series

x n = ar (n-1) (1) x 2 = 750 = ar 1 (2) x 5 = -6 = ar 4 divide second equation by first-6/750 = r 3 r 3 = -0.008r= -0.2Insert into first equation.750 = a * -0.2a = -3750Sum to infinite series = a(1/(1-r))(in...
HP
Answered by Henry P. • Maths tutor
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One important question type to be able to answer is integrating squared trig functions. like cos^2(x)

This question requires selecting the correct double angle formulae. cos(2x)=2cos^2(x)-1 is rearranged to 1/2(cos(2x)+1) this can now be integrated with the students knowledge of standard integrals. Cos integ...
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Answered by Andrew R. • Maths tutor
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