MATH 151 Engineering Mathematics I
Week In Review
Fall, 2015, Problem Set 1 (Appendix D, 1.1)
JoungDong Kim
1. If f (x) = x − x2 , evaluate
f (x + h) − f (x)
.
h
1
2. Find the domain of following functions.
(a) f (x) =
2
3x − 5
(b) g(x) =
√
4
(c) h(x) =
x+2
x2 − 1
7 − 3x
√
3
x−1
(d) k(x) = √
x+4
2
3. Convert from degrees to radians or radians to degrees.
(a) 210◦
(b) 900◦
(c) −
7π
2
(d) 4π
4. If cos x = − 13 , π < x <
3π
, find the remaining trigonometric functions.
2
3
5. Prove each identity.
(a) (sin x + cos x)2 = 1 + sin 2x
(b) cot2 x + sec2 x = tan2 x + csc2 x
4
6. Solve the following equations for x, 0 ≤ x ≤ 2π.
(a) 2 cos x − 1 = 0
(b) sin 2x = cos x
(c) 2 + cos 2x = 3 cos x
5
−→
7. Find a vector AB.
(a) A(−3, 4), B(−1, 0)
(b) A(4, −1), B(1, 2)
8. If ~a = h−1, 2i and ~b = h4, 3i, find |~a|, ~a + ~b, ~a − ~b, and 3~a + 4~b.
6
9. If |~r| = 2, and ~r makes an angle of 210◦ with the positive x-axis, find the component of the vector
~r.
10. If ~a = h3, −4i, find a vector with length 2 in the direction of ~a.
7
11. A woman walks due west on the deck of a ship at 3 mi/h. The ship is moving north at a speed
of 22 mi/h. Find the speed and direction of the woman relative to the surface of the water.
8