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MATH 141: TEST 2
Name
Instructions and Point Values: Put your name in the space provided ab ove. Check that you have 6 (di erent) test pages. Work each problem b elow and show ALL of your work. You do not need to simplify your answers. Do NOT use a calculator.
Problem (1) is worth 14 p oints. Problem (2) is worth 9 p oints. Problem (3) is worth 12 p oints. Problem (4) is worth 18 p oints. Problem (5) is worth 29 p oints. Problem (6) is worth 18 p oints.
(1) (a) Calculate lim x!
2 x + 1 x + 3
. (SHOW WORK!!)
(b) Calculate lim x!
p
x^4 + 3 x^2 2 x x^2.
(2) Calculate dy for y = sin (x^2 + 1).
(3) Calculate
R (3x + 2)^6 dx.
(5) For this page and the next page, f (x) = 3 x^4 + 8 x^3 + 6 x^2.
(a) What are the critical p oints of f (x)?
(b) Where is f (x) increasing?
(c) Where is f (x) decreasing?
(d) What are the lo cal maximum values of f (x)?
(e) What are the lo cal minimum values of f (x)?
(f ) Where is f (x) concave up?
(g) Where is f (x) concave down?
(h) What are the x-co ordinates for the in ection p oints of f (x)?
(i) Graph f (x) b elow.
