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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
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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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The cubic polynomial f(x) is defined by f(x) = 2x^3 -7x^2 + 2x + 3. Given that (x-3) is a factor of f(x), express f(x) in factorised form.

f(x) = (x-3)(2x^2 - x - 1)f(x) = (x-3)(2x +1)(x-1)x = 3, -1/2, 1 are roots of the cubic equation.
OM
Answered by Oliver M. • Maths tutor
9751 Views

Solve the follow simultaneous equation:4x + y= 4 and 2x + y= 8

4x + y= 42x + y = 8 y= 4-4xy= 8 -2x4- 4x = 8 -2x-4 = 2xx= -2y= 12
AK
Answered by Aatifa K. • Maths tutor
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