Chapter 1.1, Problem 3E

7. Evaluate the following limits and justify each step. (a) lim (3x²+2x+1) 1 x²+4x-12 (b) lim 1 2 x² - 2x t-√√3t+4 (c) lim t-0 4-t x²-6x+5 (d) lim (e) lim x 5 x-5 x→2 x²+2x+3 4u+1-3 (f) lim u➡2 u-2 1 (g) lim x-3 2 x 55 x - 7x4 +4 (h) lim xx 5x+2x-1 x+1 (i) lim x²-2x+5 - 7x8+4x7 +5x

6. Given the following graph f(x). (-2,2) 2- -5 -3 -2 (-2,-1) -1 (0,1) -2- 1 (3,0) 2 3 4 5 (3,-1) א X Compute each of the following. (a) f(-2) (b) lim f(x) #129 (c) lim f(x) *→12+ (d) lim f(x) 811H (e) f(0) (f) lim f(x) 8011 (m) Is the function continuous at x = -2,0,3? Why or why not? (g) lim f(x) +0x (h) lim f(x) x 0 (i) f(3) (j) lim f(x) x-3- (k) lim f(x) x+3+ (1) lim f(x) #13

3. Compute the profit corresponding to 12,000 units. 5. A rectangular box is to have a square base and a volume of 20 ft3. The material for the base costs $0.30 per ft2, the material for the sides cost $0.10 per ft2, and the material for the top costs $0.20 per ft2. Letting a denote the length of one side of the base, find a function in the variable x giving the cost of constructing the box. 6. Given the following graph f(x).