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Find the equation of the line perpendicular to the line y= 3x + 5 that passes through the point (-1,4)

Logically work through the problem: 1) Plot all the information that is available so you can visualise the problem better (always encouraged for graphical questions) 2) Understand that the gradient of the pe...
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Answered by Chagall C. • Maths tutor
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Given the function f(x)=λx^3 + 9, for λ other than zero, find the inflection point of the graph in terms of λ. How does the slope of the line tangent to the inflection point changes as λ varies from 0 to 1?

f'(x) = 3λx^2f''(x) = 6λxFor the inflection point (x 0 ,y 0 ), it is true that f''(x 0 )=0 so 6λx o =0 => x 0 = 0 (since λ cannot be zero)Therefore, the infelction point is (0,f(0)) => (0,9)The second ...
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Answered by Claire D. • Maths tutor
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By expressing cos(2x) in terms of cos(x) find the exact value of the integral of cos(2x)/cos^2(x) between the bounds pi/4 and pi/3.

cos(2x)=cos 2 (x)-sin 2 (x)=2cos 2 (x)-1 Therefore:cos(2x)/cos 2 (x)=(2cos 2 (x)-1)/cos 2 (x)=2cos 2 (x)/cos 2 (x) - 1/cos 2 (x)=2 - 1/cos 2 (x)=2 - sec 2 (x) Integral of sec 2 (x) = tan(x) Integral of 2 = 2...
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Answered by Hugo F. • Maths tutor
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How do I differentiate an expression of the form y = (ax+b)^n?

In order to differentiate this we need to use the chain rule- first let u = ax + b. Then differentiating, du/dx = a. By substituting into the original expression, we can obtain y = u^n. Differentiating that ...
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Answered by Sam C. • Maths tutor
12383 Views

Find dy/dx if y= sinx/2x+1

The quotient rule will need to be applied here.let u = sinx and let v = 2x+1du/dx = cosx and dv/dx =2thus using the quotient rule: (vdu/dx- udv/dx)/v^2(2xcosx +cosx - 2sinx)/ (2x+1)^2
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Answered by Sam T. • Maths tutor
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