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# Integration and Differentiation

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7. Evaluate y = Integration-sign e^(ax+b) dx .

11. Find the area of Recordi's new exponential pool, which is bounded by y=e^x, y=0, x=0 and x=3.

12. Find dy/dx for y=x^2 e^-x . Find points where the curve has horizontal tangents.

13. Find out how many bacteria there will be at time t in the gremlin's bacteria dish (dn/dt = 3n; t=0 when n=10; t is measured in hours.) How many bacteria will there be after 5 hours?

https://brainmass.com/math/integrals/integration-differentiation-exponential-functions-333763

#### Solution Preview

7. y=e^(ax+b)/a+C
11.∫_0^3▒〖e^x dx〗=e^x |_0^3=e^3-e^0=e^3-1
12. dy/dx=2xe^(-x)-x^2 e^(-x)=(2x-x^2 ) e^(-x)
The ...

#### Solution Summary

The expert integrates and differentiates exponential functions.

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