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Differentiate of Functions and Equations

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1) Solve the following equation for x. ( five points)

a) b)

2) Differentiate the following functions ( five points)
a) b)

3) Sketch the following function domain________________ (15 points)
x-intercept _________________extra
y-intercept__________________
min or max__________________
inflection points____________
interval of inc., dec.________________

4) Find the equation of the tangent line (Ten points)
, at (0,1/3)

5) Differentiate the following functions ( five points)
a) use logarithmic to differentiate b)

6) Katlin invested $9000 at 11% compounded continuously until she had $19,000, if Jordan wanted to also invest his $9000 dollars at 9% compounded continuously how long would it take him to double his money? How long did it take Kayla? (Ten points)

7) The half life of PU-666 is 7,324 years. (ten points)
a) A sample of PU-666 has a mass of 50 mg. Find a formula for the mass of the sample after t years.
b) Find the mass after 2000. Years
c) When will the mass be reduced to 15 mg.?

Calculate the definite integrals five points each

8) a) b)

9) Calculate the definite integral
a) b)

10) Find the indefinite integrals. ( five points)

a) b)

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The expert differentiates functions and equations.

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