Questions from General Calculus

Q: Find a + b, 4a + 2b, |a |,

Find a + b, 4a + 2b, |a |, and |a - b |. a = 5i + 3j, b = -i - 2j

Q: Figure 16 gives a geometric demonstration of Property 2 of vectors.

Figure 16 gives a geometric demonstration of Property 2 of vectors. Use components to give an algebraic proof of this fact for the case n = 2.

Q: Prove Property 5 of vectors algebraically for the case n = 3

Prove Property 5 of vectors algebraically for the case n = 3. Then use similar triangles to give a geometric proof.

Q: The cost function for a certain commodity is C(q

The cost function for a certain commodity is C(q) = 84 + 0.16q - 0.0006q2 + 0.000003q3 (a) Find and interpret C9s100d. (b) Compare C’(100) with the cost of producing the 101st item.

Q: Use vectors to prove that the line joining the midpoints of two

Use vectors to prove that the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

Q: Find a + b, 4a + 2b, |a |,

Find a + b, 4a + 2b, |a |, and |a - b |. a = 4i - 3j + 2k, b = 2i - 4k

Q: Find a + b, 4a + 2b, |a |,

Find a + b, 4a + 2b, |a |, and |a - b |. a = 8, 1, −4 , b = 5, −2, 1

Q: Find a unit vector that has the same direction as the given

Find a unit vector that has the same direction as the given vector. 8i - j + 4k

Q: Find the vector that has the same direction as 6,

Find the vector that has the same direction as 6, 2, −3 but has length 4.

Q: A particle moves along a line with velocity function v(t

A particle moves along a line with velocity function v(t) = t2 - t, where v is measured in meters per second. Find (a) the displacement and (b) the distance traveled by the particle during the time in...