only for 9,11,14 please

8. Use algebraic methods to evaluate each limit (if it exists). i. lim 2x- + 1 x- - 4 r - 5 d. lim 1 42 2- x - 2 b. lim x- 3 x-2 Vx+6 -3 e. lim 8 C. lim f. lim VI+4 - V4-x 8-3x+3 9. Determine the derivative of each function from first principles. a. f(x) = 3x + x+ 1 b. /(@) = = 10. Determine the derivative of each function. i. y= x - 4x + 5x + 2 d. y= (x + 3) (4x) + 5x + 1 ) b. y = V2x + 1 e. y= (4x + 1)5 (3x - 2)3 2x C. J= x+3 f. y = [x + (2x + 1)315 1 1. Determine the equation of the tangent to y =; 18 (x + 2)2 at the point (1 , 2). 12. Determine the slope of the tangent toy - x' + 9x + 9 at the point where the curve intersects the line y = 3x. 13. In 1980, the population of Littletown, Ontario, was 1100. After a time r, in years, the population was given by p() = 2 + 6r + 1100. A. Determine p'(f), the function that describes the rate of change of the population at time f. b. Determine the rate of change of the population at the start of 1990. C. At the beginning of what year was the rate of change of the population 110 people per year? 14. Determine f' and f" for each function. a. f(x) = x - 5x + x+ 12 c. A(x) = 4 VX b. f(x) d. f(x) = x4 - 15. Determine the extreme values of each function on the given interval. a. f(x) =1+ (x+3), -2=x=6 c. f(x) = 1 x= [0,4] b. f(x) = x + 15x59 d. f(x) = 2 sin 4x + 3, x= [0, w]