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f(x)=2x^3-7x^2+4x+4, prove that (x-2) is a factor and factorise f(x) completely

if (X-2) is a factor, f(2)=0 2 2^3-7 2^2+4*2+4= 16-28+8+4=0 therefore (x-2) is a factor. 2x^3-7x^2+4x+4=(x-2)(2x^2-3x-2)=(x-2)(2x+1)(x-2)
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Answered by Bryce P. • Maths tutor
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Find the derivation of (sinx)(e^2x)

Because there are two forms of x , the form uv'+vu' must be used. If y=sinx , dy/dx=cosx If y=e^kx , dy/dx=ke^kx Therefore dy/dx=(sinx)(2e^2x)+(e^2x)(cosx)
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Answered by Eric B. • Maths tutor
5310 Views

Use logarithms to solve the equation 2^5x = 3^2x+1 , giving the answer correct to 3 significant figures.

Firstly, I would make sure that the student is aware of the basic conept of logarithims and run through the basic "laws" of logarithims to make sure that they have the knowledge they need to answer...
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Answered by Shubhayu G. • Maths tutor
14095 Views

What are complex and imaginary numbers and how are they different from normal (real) numbers?

When you think of a number line, zero lies at the centre and the positive numbers stretch off to the right, while negative numbers go off left. This is a representation of real numbers, including both ration...
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Answered by Tutor59493 D. • Maths tutor
3977 Views

How do you integrate ln(x) with respect to x?

This integral must be done using integration by parts. Therefore, we set u=ln(x) and dv=dx, which gives du=1/x and v=x. Then, using the integration by parts formula the integral now equals x*ln(x)-int[dx]. T...
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Answered by Oliver H. • Maths tutor
6170 Views