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

f(x) = x 3 + 2x 2 - x - 2 Use the factor theorem to test for f(1) = 0 f(1) = 1 3 + 2*1 2 - 1 - 2 = 0 Therefore x = 1 is a solution and (x-1) is a factor of f(x) Now factorise f(x) x 3 + 2x 2 - x - 2 = (x-1)(...
ES
Answered by Elena S. • Maths tutor
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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
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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:a 7 + 7a 6 b + 21a 5 b 2 + 35a 4 b 3 + 35a 3 b 4 + 21a 2 b 5 + 7ab 6 + b 7 , where a=x a...
JW
Answered by Josef W. • Maths tutor
8761 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 re...
NM
Answered by Neil M. • Maths tutor
3608 Views

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

f(x) = 8x 3 + 1 / x 3 >>> f(x) = 8x 3 + x -3 f'(x) = 3(8x 2 ) + -3(x -4 ) >>> f'(x) = 24x 2 - 3x -4 f''(x) = 2(24x 1 ) - 4(-3x -5 ) Final Answer, f''(x) = 48x + 12x -5
SS
Answered by Sam S. • Maths tutor
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