MAC 2312 Midterm: MAC2312 C96 Test 3
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A medication being given to a patient is absorbed into the blood at the constant rate of 3 mg/hr. The patient"s liver is removing the same medication at a rate proportional to the amount in the blood (2 mg/hr per mg in the blood). Assuming there is initially 0 mg in the blood, set up and solve the di erential equation for the amount of medication in the blood. Sketch the graph of the solution: (15 pts. ) Find the taylor polynomial of degree 4 about x = 1 for f (x) = 5 ln x: (15 pts. ) Find a third-degree polynomial approximation about x = 0 to approximate the solution to the di erential equation y = y2 15x 1; y(0) = 2: (20 pts. ) Evaluate the limits. (a) lim x x + 3 x 2 x (c) lim x 0+ xx+1 (b) lim x 0 (d) lim x 0 ln(1 + 2x) x sin x2.
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No common factor m^5 (20m^4 + 6m^2 +20) 2m^5 (10m^4 + 3m^2 +10) |
(0, 0) (0, 1) (1, 1) |
121p^2 + 88p - 16 121p^2 - 16 121p^2 - 88p -16 |
(7, -7) (9, -9) (-7, 7) |
(18x^2 - 2)(x - 5) (3x^2 - 2)(6x - 5) x(18x + 2)(x +5) |
x^2 + 8xy + 8y^2 x^2 + 8xy + 15y^2 x + 8xy + 15y |
54x^14 + 72x^9 54x^14 + 72x^9 -42x^7 54x^14 + 12x^2 -7 |
(15x - 2)(x + 4) (3x - 2)(5x + 4) (3x + 2)(5x -4) |
Trinomial, degree 3 Trinomial, degree18 Trinomial, degree11 |
12x^42 + 9 10x^26 - 2x^14 + 4x^12 +9 4x^8 + 4x^7 + 4x^6 +9 |
-3n^5 + 11n^3 - 3 5n^8 -3n^5 + 11n^3 -9 |
(-2, 4) (-1, 3) No solution |
(4, 1) (4, 0) No solution |
False |
False |
False |
False |
False |
False |
False |