Knowing that lim x→1 3x + 2 = 5, what values of x guarantee that f(x) = 3x + 2 is within:

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Math problems

Section 1.0 Problem #2

  1. (a) What is the slope of the line through (−2, 4) and (x, y) for y = x 2 when: i. x = −1.98? ii. x = −2.03? iii. x = −2 + h? (b) What happens to this last slope when h is very small (close to 0)? (c) Sketch the graph of y = x 2 for x near −2.

Section 1.4 Problem #2

  1. Knowing that lim x→1 3x + 2 = 5, what values of x guarantee that f(x) = 3x + 2 is within: (a) 1 unit of 5? (b) 0.6 units of 5? (c) 0.09 units of 5? (d) e units of 5?