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If the complex number z = 5 + 4i, work out 1/z.

1/(5 + 4i) * (5 - 4i)/(5 - 4i) = (5 - 4i)/41
OG
3767 Views

How to integrate ln(x)?

You need to use a clever trick for this! Write ln(x) as 1 ln(x), and use integration by parts:u=ln(x) v'=1u'=1/x v=xThen applying the formula we obtain∫ln(x)dx = x ln(x) - ∫[(1/x) x] dx = = x ln(x) - ∫1 dx =...
KW
3605 Views

Differentiate arcsin(2x) using the fact that 2x=sin(y)

Differentiate implicitly on both sides with respect to x to get: 2=cos(y) • (dy/dx). Divide by cos(y) on both sides to get: dy/dx=2/cos(y). Use the trigonometric identity cos^2(y)+sin^2(y)=1 rearranged to co...
LO
3669 Views

f(x)=ln(x). Find the area underneath the curve f(x) between 1 and 2.

We cannot dirrectly intergrate ln(x), so instead we intergrate 1 ln(x) using intergration by parts. The formula for intergration by parts is: ∫ (u dv/dx) dx = uv − ∫ v du/dx dx . We let u=ln(x) so that du/dx...
AT
3409 Views

Let f(x)=x^x for x>0, then find f'(x) for all x>0.

A common misconception from many students when tackling this problem is that they think the usual 'power rule' works. However, in this case the power is itself a function of x and not just a constant, so thi...
MF
2542 Views