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integral of (tan(x))dx using the substitution u = cos(x)

given u = cos(x), therefore du/dx=-sin(x), as tan(x)=sin(x)/cos(x), can rewrite tan(x)=(-du/dx)/u, therefore integral can become [(-1/u)du], after inegrating you are left with -ln(u)+c, therefore ln(1/u)+c, ...
FR
Answered by Frederick R. • Maths tutor
5162 Views

f(x) = x^x, find f'(3).

Therefore, y = x x can then natural log both sides leaving ln(y) = xln(x) then differentiating both sides wrst to x d/dx(ln(y)=xln(x))we are then left with this expression (dy/dx)(1/y)=ln(x)+1 multiplying up...
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Answered by Frederick R. • Maths tutor
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A 10 kilogram block slides down a 30 degree inclined slope, the slope has a coefficient of friction of 0.2. Calculcate the blocks acceleration down the slope.

Resolving all forces in the vertical gives the normal force as 10gcos(30). Resolving all forces normal to the slope gives the frictional force as 2gcos(30) (given Friction = mu*R). Using second law, F=ma. 10...
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Answered by Frederick R. • Maths tutor
3837 Views

What are the stages of the cell cycle?

Interphase and Mitosis make up the cell cycle.Interphase includes 3 phases- G1- Cell growth phase and this is where cell multiply their organelles and their cytoplasms expand;S phase- DNA synthesis phase and...
JB
Answered by Jade B. • Biology tutor
4959 Views

Explain the trend in the first ionisation energies of the group 1 elements

The general trend is a decrease in first ionisation energy, which is because as you descend the group the number of energy levels surrounding the positively charged nucleus increases. This means that the out...
CB
Answered by Caitlin B. • Chemistry tutor
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