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if a^x= b^y = (ab)^(xy) prove that x+y =1

ln(a^x) = ln(b^y) = ln((ab)^(xy)) xln(a) = xyln(ab) ln(a) = yln(ab) = y(ln(a) + ln(b)) y = ln(a)/(ln(a)+ln(b)) with same analysis for ln(b^y): ln(b) = x(ln(a) + ln(b))x = ln(b)/(ln(a)+ln(b)) x + y = (ln(a) +...
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Answered by Scott C. • Maths tutor
6308 Views

Find the first 3 terms, in ascending powers of x, of the binomial expansion of (2 – 9x)^4 giving each term in its simplest form.

(2-9x)^4 [2(1-4.5x)]^4 (2^4)(1-4.5x)^4 Using the binomial expansion formula 16[1+(4*(-4.5x))+(((4*(4-1))/(1 2))) (-4.5x)^2] 16[1-18x+121.5x^2] 16-288x+1944x^2
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Answered by Lauren J. • Maths tutor
8523 Views

How to find gradient of functions

To find the gradient of a function, that has constant gradient you pick any two points. You label both the x and y co-ordinates of these two points.Then you subtract the y co-ordinates of these two points. Y...
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Answered by Sinan H. • Maths tutor
4486 Views

Integrate the function f(x) where f(x)= x^2 +sin(x) + sin^2(x)

Answer: Integral= x 3 /3+ x/2 - cos(x) -1/4 sin(2x) + C Using the general rule that integrating x n results in x (n+1) /(n+1), x 2 integrates to x 3 /3.sin(x) is integrated to -cos(x)To integrate sin 2 (x), ...
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Answered by Charlie H. • Maths tutor
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Determine the coordinates of all the stationary points of the function f(x) = (1/3)*x^3+x^2-3*x+1 and state whether they are a maximum or a minimum.

To find the answer you must first differentiate the function and set this equal to zero. This forms the quadratic equation x^2+2 x-3=0 which can then be solved either by factorisation or by using the quadrat...
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Answered by Alex N. • Maths tutor
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