Math 121 Test 3 2018
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Math 121 Test 3
November 20, 2018
1. (15 points)
(a) A linear approximation gives f (2.01) s 4.5. If f (2) = 4.3, what is f\ (2)?
(b) Find the absolute max and absolute min of y = x3 _ 12x + 5 on the interval 1 < x < 4.
(c) Apply the Mean Value Theorem to find c for the function
x _ 4
g(x) =
on the following intervals if possible. If not, explain why not.
i. [0, 5]
ii. [4, 6]
2. (20 points)
(a) Use the following information to sketch the graph. Label all crit- ical points with “c.p.” and all inflection points with “i.p.” . Domain is (_o, 2) u (2, o), f (_1) = 3, f (_2) = 2
x-intercepts: (1, 0), (3, 0), y-intercepts: (0, 2),
Vertical asymptotes: x = 2,
lim f (x) = 1, lim f (x) = 0
f/ (x) < 0 for x in (_1, 2), f/ (_1) = 0
f/ (x) > 0 for x in (_o, _1) u (2, o)
f// (x) < 0 for x in (_2, 2) u (2, o), f// (_2) = 0
f// (x) > 0 for x in (_o, _2)
(b) lim (1 _ tan x) sec 2x
x→π/4
(c) x ╱ _ 、
3. (15 points)
(a) Find the
perimeter
dimensions of the rectangle with the largest possible that can be inscribed in a semicircle of radius 1.
(b) A differentiable function satisfies f (3) = 0.2 and f\ (3) = 10. If Newton’s method is applied to f (x) starting at x0 = 3, what is the value of x1 ?
4. (15 points)
(a) Compute lim
(b) Compute x ╱ _ 、
(c) Find the distance traveled if v(t) = cos(2t) m/s for 0 < t < 3T seconds.
5. (20 points)
(a) Compute dx, if f (1) = 1 and f (2) = e
4
(b) Compute ^4x _ x2 dx
2
(c) Compute dx
(d) Compute
│ ^3x2 + 1\ dx
6. (15 points)
(a) Compute dx
(b) Compute (3x + 4)(x + 3)40 dx
(c) Compute
sec2 x
^1 _ tan2 x
dx
2022-11-19