# How to calculate this? #int_0^piarcsin(cos^3x)dx#

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- If the instantaneous rate of change of a population is #50t^2 - 100t^(3/2)# (measured in individuals per year) and the initial population is 25000 then what is the population after t years?
- How do you find the instantaneous rate of change for the volume of a growing spherical cell given by #v = (4/3) (pi) r^3# when r is 5?
- How do you find the slope of a tangent line to the graph of the function #3xy-2x+3y^2=5# at (2,1)?
- How do you find the slope of a tangent line to the graph of the function #f(x)= (1+2x^(1/2)) / (1+x^(3/2))# at (4, 5/9)?
- Using the definition of a derivative how do you calculate the derivative of #f(x) = x^2 + x#?

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