Search over 10,000 free study notes

Heat is lost in the fluid through Conduction convection radiation and evaporation. The silvered surfaces reflect infrared rays back into the liquid keeping heat in the fluid reducing heat lost by radiatio...

First notice that f(x) = u/v. So f'(x) =[ v(u') - u(v')]/v² (the Quotient rule). After working it out, we find f'(x) = 6x/(x² + 5)² (the steps can be shown on the whiteboa...

Take u = 1+3x² , this gives that y = u^1/3 . By the chain rule we have that dy/dx = dy/du * du/dx. By differentiating y = u^1/3 with respect to u giv...

first of all we have to recognise the general form of the equation, similar to the equation of a line but we just have to add one more term due to the fact that it is a second degree equation: y=ax^2<...

For this you’ll want to use the integration by parts method. In this the form u use is:integral of udv = uv - integral of vduTherefore we can rewrite the integral as ln(x)*1 labelling 1 as dv and ln(x) as...