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Prove that, if 1 + 3x^2 + x^3 < (1+x)^3, then x>0

(1+x)^3 = x^3 + 3x^2 + 3x + 1 (Can be calculated straight away by binomial method or by multiplying brackets individually) if (1+x)^3 &gt; 1 + 3x^2 + x^3then: x^3 + 3x^2 + 3x + 1 &gt; 1 + 3x^2 + x^3 3x &gt; ...
VT
Answered by Vigneswaran T. • Maths tutor
16453 Views

Differentiate y = xe^(2x).

We want to find dy/dx. We find this using the product rule by setting the functions f(x) = x and g(x) = e 2x . With these functions, we can write the equation as y = f(x)g(x), so by applying the product rule...
ML
Answered by Matthew L. • Maths tutor
34127 Views

what is the integral of ln(x)

answer may not be obvious at first, but by using intergration by parts, treating part 1 as lnx and part 2 as 1, you will get xlnx-1
AF
Answered by Anthony F. • Maths tutor
3540 Views

A curve has the equation 6x^(3/2) + 5y^2 = 2 (a) By differentiating implicitly, find dy/dx in terms of x and y. (b) Hence, find the gradient of the curve at the point (4, 3).

(a) To differentiate implicitly, differentiate x’s as normal and differentiate y’s with respect to y before multiplying by dy/dx. Therefore the differentiating the curve gives 9x^(1/2) + 10y*(dy/dx) = 0 whic...
ML
Answered by Matthew L. • Maths tutor
4011 Views

Find the turning points of the curve y = 3x^4 - 8x^3 -3

Differentiate to get:dy/dx = 12x^3 -24x^2Factorise and set equal to 0:12x^2(x-2) = 0Solve to get x = 2 and x =0.
DC
Answered by Daniel C. • Maths tutor
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