( Please answer these 10 questions ID really appreciate it)

1.Determine the average rate of change of y in the function y = 2 x ³ + 7 x ² + 2x 3 over the interval [3,5].

2. Given the function f(x) = 2 x ² + 3x + 1,

a. Find the instantaneous rate of change when x = 1.

b. Find the value of the derivative when x = 1.

c. What did you notice?

3. Explain the difference between a secant line and a tangent line. How do they relate to the rate of change of a function? Include a sketch of each type of line in your solution.

4. The path of a baseball relative to the ground can be modelled by the function d(t) = t² + 8t + 1, where d(t) represents the height of the ball in metres, and t represents time in seconds.

a. Find the average rate of change of the ball between 1 and 3 seconds.

b. Using the secant method, find the instantaneous rate of change at 2 seconds.

5. a. Evaluate lim (3x' + 7x-16) x- 2 b. What is the meaning of this value? 6. Evaluate the following limits. x - 16 a. lim x-4 x-4 8x3 -5x2 +17 b. lim X->00 6x3+ 2x2 -4x 49 + h-7 C. lim h-0 h y' - 8 d. lim y-2 2v2 - 7y+12 4 2 e. lim 2+ h h 7. Find the slope of the tangent line at point (-2,2) on the curve f(x) = 2x2 + 3x 8. Find the derivative of the function f(x) = x2 - 10x + 3 using First Principles