# Math 18

Math 180 -Assignment #5 Due: 10:00a, Monday, April 26th, 2021 ************************************************************************** READ AND FOLLOW DIRECTIONS **Complete solutions using proper notation will be required to receive full credit. *Please clearly identify your final answers. Circle your final answers where appropriate. **Please start each NUMBERED PROBLEM on a new page. *Please put your problems in numerical order before submitting them as a single PDF or Word Document via Blackboard. **Do NOT wait until the last minute. Late submissions will receive severe reductions. *Each numbered problem will be graded on a 10-point scale. The total will be scaled to 100 points. ***************************************************************************** #1.) Evaluate the integral. You are required to show the u-substitution process.  (7x + 4)5  dx 9 #2.) Evaluate the integral. You are required to show the u-substitution process.  tan3 x  sec2 x  dx #3.) Evaluate the integral. You are required to show the u-substitution process. 8  3×2 + 4  dx 0 #4.) Evaluate the integral. You are required to show the u-substitution process. 6 2 1  dx 4x +1 NOTE: #1C is the ONLY answer on this assignment where decimals can be considered. #5.) Choose the Trapezoid or Simpson’s Rule, but NOT both. Make sure it is clear WHICH Rule you are using. The next page is intentionally left blank for working space, if needed. 5 A.) Approximate  −1 3  dx , n = 6 2+ x B.) Find the maximum error possible for the method you chose. 5 C.) Find an interval showing the possible values for  −1 Derivatives of f ( x ) = f ‘( x) = − f iv ( x ) = 3 (2 + x) 2 72 5 (2 + x) 3  dx. 2+ x 3 you may or may not find useful. 2+ x 6 f ” ( x ) = 3 (2 + x) f v ( x) = − 360 6 (2 + x) f ”’ ( x ) = − f vi ( x ) = 18 (2 + x) 4 2160 7 (2 + x) #6.) Use logarithmic differentiation to find y= 1 − x2 , 2 2+ x −1  x  1 dy . dx #7.) Choose A or B, but NOT Both. Evaluate the integral. Show all necessary work. A.)  6 x + 15  dx 2x +1 e5 B.)  x  ln ( x4 )  dx e2 1 #8.) Choose A or B, but NOT Both. Find the derivative.  3 + e2 x   A.) y = ln   3 − e2 x    e5 x B.) F ( x ) =  ln (3t + 7)  dt, Hint: 2nd FTC 3 #9.) Evaluate each integral.  e3x  e3x − 4  dx #10.) Evaluate each integral. ln3 ( ln2 ) 2 e3x − 4  dx
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