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f(x) = x^3 - 13x^2 + 55x - 75 , find the gradient of the tangent at x=3

f(x) = yy= x 3 - 13x 2 + 55x - 751) find f'(x) [=dy/dx] Differentiation is (1) multiplying the coefficient by the original power --> 2) reducing the original power by 1dy/dx = 3x 2 - 26x + 55 2) find f'(3...
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Answered by Kiitan O. • Maths tutor
4008 Views

Solve 2sin2θ = 1 + cos2θ for 0° ≤ θ ≤ 180°

sin2θ = 2sinθcosθ (double angle formula for sine)cos2θ = cos 2 θ - sin 2 θ (double angle formula for cosine) = 2cos 2 θ - 1 (utilising the trignometric identity sin 2 θ + cos 2 θ = 1) We substitute these int...
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Answered by Samuel N. • Maths tutor
13511 Views

Integrate the function f(x) = 1/(4x-1)

t Using the fact that d/dx ( ln g(x)) = g'(x)/g(x), we can see that the integral of this function will be an ln function. From observing f(x) we see that if the answer was ln(4x-1) then f(x) would need to be...
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Answered by Sachin V. • Maths tutor
9590 Views

How do I integrate 4x*exp(x^2 - 1) with respect to x?

During the session I would go step by step through the integration by substitution.
AS
Answered by Anmol S. • Maths tutor
3818 Views

Integrate (1 - x^2)^(-0.5)dx within the limits 0 and 1

The answer is π/2. The key trick to solving this problem is to change variables by using the substitution x = sin(θ). We then need to change the differential and the limits too.
CW
Answered by Cameron W. • Maths tutor
4184 Views