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Maths
A Level

f(x) = x^3+2x^2-x-2 . Solve for f(x) = 0

f(x) = x3 + 2x2 - x - 2 Use the factor theorem to test for f(1) = 0 f(1) = 13 + 2*12 - 1 - 2 = 0 Therefore x = 1 is a solution and (x-1) is a factor of f(x) Now...

ES
Answered by Elena S. • Maths tutor
4533 Views

If y=2x+4x^3+3x^4 and z=(1+x)^2, find dy/dx and dz/dx.

Differentiation dy/dx = 2+12x^2+12x^3
Chain ruleu = 1+xz=u^2dz/dx = dz/du * du/dx = 2u * 1 = 2(1+x)

Answered by • Maths tutor
3541 Views

What is the coefficient of x^4 in the expansion of (x+3)^7

Start by expanding (a+b)7, using Pascal's Triangle or the binomial coefficient function to work out the coefficients:a7 + 7a6b + 21a5b2 + 35a4

JW
Answered by Josef W. • Maths tutor
7764 Views

Integrate 1/(1 - 3*x) with respect to x

First substitute: u = 1 - 3xNext calculate: du/dx = -3 .... therefore dx = (-1/3) * duNow re-arrange the expression: Integrate 1/u * ( -1/3)*duNext recall the integral of 1/x is the natural logarithm, and...

NM
Answered by Neil M. • Maths tutor
3027 Views

If, f(x) = 8x^3 + 1 / x^3 . Find f''(x).

f(x) = 8x3 + 1 / x3 >>> f(x) = 8x3 + x-3
f'(x) = 3(8x2 ) + -3(x-4) >>> f'(x) = 24...

SS
Answered by Sam S. • Maths tutor
4454 Views

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