1. Prove by Mathematical Induction that 4+8+12+ ...+ (4n) = 2n(n+1) is true for all positive integers, n .
1. Prove by Mathematical Induction that 4+8+12+ ...+ (4n) = 2n(n+1) is true for all positive integers, n .
2. Expand and simplify (2x - 5y)3
3. Sketch the polynomial
4. A rational function is given as h(x) = x/ (x-1)(x-3). Sketch the graph of h(x), showing all the intercepts and asymptotes clearly.
5. Prove the following
6. Express y = 6Cos(theta) + 8Sin(theta) in the form y = rSin(theta + alpha), where alpha is an acute
7. Solve 2Sin 2x - 1 = 0 for 0 <_ x <_360a .
8. A
i. Express z in polar form.
ii. Use De Moivre’s Theorem to find z5 . Hint: zn = rn (Cosn(theta) + iSin n(theta))
9. Given v = 1-3i and w = -1+5i, find
i. v+w
ii. |v|
10. A sequence an is defined by an = n+2/4n+1
i. Find the first 4 terms of the sequence
ii. Simplify an+1 - an and determine whether the sequence is increasing or decreasing.
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
