Suppose f, f', g, and g' have the following values: 1 2 3 4 f(x) 8 2 1 -8 f'(x) g(x) 10 -7 - 2 6 -6 – 253 - 252 - 246 - 248 - 262 - 64 56 14 - 15 23 (2),6 At the half-time show for a Milwaukee College football game, a balloon will travel along a path with equation z + y = f(x)g(x) and will be released at the point where x = 2. To ensure the safety of the crowd, Sophia needs the equation of the line tangent to the graph of 2° + y° = f(x)g(x) at x = 2 For this question, if you choose to use decimals, be sure that you round your numbers to at least 4 decimal places. The equation of the tangent line is:

(15) Determine whether or not the functions y₁ 4x³, y2 = π, y3 = 12x², and y4 = 24x are linearly independent on any interval. Show all work to support your answer.

I Eliminate the arbitrary constants y = x²+ ax + be*

5. St V1- t dt

If fxy (x, y) = y for 0 2X – 2) =

Determine which of the following pairs of functions are linearly independent. 1. f(x) = x² g(x) = 4|x|² NO_ANSWER NO_ANSWER NO_ANSWER NO_ANSWER " ✓ 2. f(x) = e4x ✓ 3. f(0) = cos(30) ✓ 4. f(t) = 3t, g(t) = |t| " g(x) = 4(x-3) 2 g(0) = 4 cos³ (0) - 4 cos(0)

1. A department store has found that its value of sales (z) depends on the number of advertisements in circulars (x) and in newspapers (y), given by z = 420x – 2x2 – 3xy - 5y2 + 640y + 1725. If the price per advertisement is RM1 in circulars and RM4 in newspapers, and the advertising budget is RM180, i) Write the Lagrangian function. ii) Find the number of advertisements in circulars and newspapers that will maximize sales subject to the budget constraint.

11. In the function y = 3x2 – 3, y is replaced by y and then y is replaced with y +2 ; the new equation in simplest form would be Oy = 6x2 – 8 Oy =2x2 – 5 Oy = 6x2 – 5 Oy = 3x2 – 8 -

6. The domain of y = v1-x2 is