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