# Math 121 Final review - Math 121 Final Review 1 Let f(x =(x...

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Chapter 2 / Exercise 88
College Algebra
Larson
Expert Verified
Math 121 Final Review 1. Let f ( x ) = ( x + 2) 2 and g ( x ) = x 3 , find: a. ( f + g )( x ) b. ( f · g )( x ) c. ( f/g )( x ) d. ( f g )( x ) e. ( g f )( x ) 2. For y = 25 x ( x 5 - 10) 2 , find all points where the tangent line is horizontal. 3. lim x 1 x 4 - x 2 x 4 - 1 4. lim θ π 2 (1 - sin θ cos θ cot θ ) 2 + θ 5. Find f 0 ( x ) for f ( x ) = 3 x - 8 x 3 1 + 5 x 2 6. Find f 0 ( x ) for f ( x ) = (sin(2 x + 1)) 3 (4 x 3 + 6 x ) 2 7. Find the maximum and minimum of f ( x ) = x x 2 + 1 on [0 , 3] 8. Find dy dx for x 3 + y 3 = 3 xy 9. Find f 0 ( x ) for f ( x ) = x 9 tan(2 x ) 10. Find f 0 ( x ) for f ( x ) = ln ( x 2 + 4) 3 cos x 11. Given the curve xy 2 - x 3 y = 6 a. Find dy dx b. Find the tangent line(s) to the curve where x = 1. c. Find the x -coordinate of each point on the curve where the tangent line is vertical. 12. It is a dark and stormy night. You are drinking hot coffee as you do your chemistry lab. You are inspecting the graph of your data when a loud clap of thunder startles you. Your coffee spills- a drop falls on to the graph and since the lab print-out is so thin the paper dissolves! There is now a hole right where the graph crosses the x -axis. You need the x -intercept for you experiment. You know the equation is f ( x ) = x 3 / 2 - 10. Use Newton’s method to find the x -intercept between 4.2 and 4.8. 13. Use a linear approximation L ( x ) to an appropriate function f ( x ), with an appropriate value of a to estimate 257. 14. Find the concavity of f ( x ) = 3 x 4 - 12 x 3 + 1 15. Sketch the graph of f ( x ) = 2( x 2 - 9) x 2 - 4 16. Compute the Riemann Sum using the right-hand end-points over the indicated interval divided into “ n sub-intervals. Also, compute the integral and compare the results. f ( x ) = 1 3 x 3 + 1; [ - 1 , 2], n = 6. 17. Z 3 2 ( x 2 + 3)( x 3 - 1) dx 18. Z (2 x 3 - 1) 5 x 2 dx
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Chapter 2 / Exercise 88
College Algebra
Larson
Expert Verified
19. Compute both the net distance and the total distance traveled between time t = 0 and time t = 10 if the velocity v ( t ) = - 32. 20. Find the volume if the area enclosed by f ( x ) = x 2 , x = 4 , x = 1 , y = - 2 is rotated about the line y = - 2 21. Find the volume if the region bounded by y = x 2 , y = - 2 x + 3 , and the y -axis in the first quadrant, is rotated about the y -axis. 22. You are at an ice cream shop. You order your favorite ice cream, chocolate chip cookie dough. You haven’t eaten all day, and begin to gobble down the ice cream. If the ice cream cone is 2 feet long and has a radius of 1 foot, how much work is required to eat all the ice cream. (The density of ice cream is ρ = 55 . 5lb/ft 3 .) 23. Find f 0 ( x ) for f ( x ) = sin( x 2 ) ln( x 2 + 3 x ) 24. Z 2 x + 1 x 2 + x + 1 dx 25. Find f 0 ( x ) by logarithmic differentiation for f ( x ) = x + 1 3 x + 2 5 x + 3 26. Find dy dx for y = ( x + 3) 3 ( x 2 - 2) 4 27. Given the following chart: x 1 2 3 4 f ( x ) 3 4 2 5 g ( x ) 1 1 4 3 f 0 ( x ) 4 2 3 2 g 0 ( x ) 2 3 1 4 If h ( x ) = ( g f )( x ), find h 0 (3) 28. For the function f ( x ) = 1 x 2 - 1 find the domain and f (5). 29. For f ( x ) = x 4 - x 2 + x , find f ( - a ) , f ( a - 1 ) , f ( a ), and f ( a 2 ). 30. If f ( x ) = x 2 + sec x and g ( x ) = sin x - cos x , find ( f g )( x ) and ( g f )( x ) 31. lim x 0 4 x cos 1 x 32. Find where the function f ( x ) = 3 q x + 5 x - 5 is continuous.