Tutor profile: Pranav B.
Integrate the following equation: f(x) = ln(x)/[x*sqt(1+(ln(x))^2]
Substitute u = 1+(lnx)^2 du= 2*ln(x)/x dx plug it in the equation f(x) = 1/2 int(1/sqt(u) du applying the power rule = sqt(u) undo substitution =sqt(1+ln(x)^2 + 1) Final answer =sqt(1+ln(x)^2 + 1) + C
Solve for the inverse of the following functions: f(x)= (3x+2)/(x-1).
y=(3x+2)/(x-1) Switch all x’s and y’s x=(3y+2)/(y-1) multiply both sides by (y-1) x(y-1)=3y+2 distribute the x on the right hand side. xy-x=3y+2 subtract 3y from both sides and add x on both sides. xy-3y=2+x Take y common on the right hand side. y(x-3)=2+x divide both sides by (x-3) y=(2+x)/(x-3) f^-1(x)=(2+x)/(x-3) [inverse of the function]
What is the difference between specific heat and specific latent heat of fusion?
- Specific heat is the amount of energy required to increase the temperature of a unit mass by 1-degree celsius. - Specific latent heat of fusion is the amount of energy required to change the state of a unit mass from solid to liquid without change in temperature.
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