Reference: Calculus and Its Applications, 12th, by Marvin L. Bittinger and David Ellenbogen Book

Elementary Applied Calculus

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Find the exact value of the integral using formulas from geometry. ( 1 + * ) dx ( 1 + x ) dx = _ (Simplify your answer.) 2a) Use the Product Rule to find the derivative of the given function. b) Find the derivative by multiplying the expressions first. F(x) = 9x (x# - 9x) a) Use the Product Rule to find the derivative of the function. Select the correct answer below and fill in the answer box(es) to complete your choice. O A. The derivative is 9x ( ) + 270x* ( ) O B. The derivative is 9x ( ) + (x4 - 9x) ( D) O C. The derivative is 9x (x - 9x) () O D. The derivative is (x4 - 9x) ( b) Multiply the expressions. 9x (x# - 9x) = (Simplify your answer.) Now take the derivative of the answer from the previous step and simplify the answer from part a. Check to make sure that the two results are the same. That is, using either approach, F'(x) =Find an equation of the line tangent to the graph of f(x) = - 3 - 4x" at ( - 5, - 103). The equation of the tangent line to the graph of f(x) = - 3 - 4x" at (- 5, - 103) is y = (Type an expression using x as the variable.)Find the future value P of The amount Po invested for time period t at interest rate k, compounded continuously. P1} =52D, t=4 years1 k=4_5% P = 5D {Round to The nearest dollar as needed] \fEvaluate. (Be sure to check by differentiating!) 1 (5+x )' 6x5 d [ (5 +x8 ) 6x5 dx = (Type an exact answer. Use parentheses to clearly denote the argument of each function.)