By Jim Hrisoulas

Trying to find directions in bladesmithing that'll placed you at the innovative of the customized blade industry? Then this definitive advisor to forging world-class blades is for you. Written through a grasp bladesmith, this e-book tells you ways to establish your forge, choose your fabrics, model grips and hilts, grind edges and lots more and plenty extra!

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10 8 6 4 2 -5 -4 -3 -2 -1 1 2 3 4 5 -2 • (−2, −5) -4 -6 • (2, −5) -8 -10 Fig. 3. Because the slope of the line is 0, the average rate of change of the function is zero between x = −2 and x = 2. The function obviously changes in value but the changes negate each other. • Find the average rate of change for f (x) = 23 x − 4 between x = −3 and x = 0 and between x = 6 and x = 12.

Although the limit of y as x approaches −3 does not exist for the graph above, both one-sided limits do exist. The limit of y as x approaches −3 from the left is 5. The limit as x approaches −3 from the right is 1. ” The notation lim f (x) = b x→a is saying, “the limit of y as x approaches a is b,” where we use f (x) for y. EXAMPLES • • lim f (x) = 12 x→7 The limit of f (x) as x approaches 7 is 12. lim (x 2 − 2x) = −1 x→1 The limit of y (or of x 2 − 2x) as x approaches 1 is −1. 14 is the graph of a function f (x).

1 • -3 Fig. 14. 49 CHAPTER 2 The Limit and Continuity 50 The notation for a one-sided limit uses a plus or minus sign as a superscript to the right of the number. 15. 5 ◦...... 4 ... ... ... ... ... ... ... ... ... ... ... .. 3 2 1 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 • ............................................................................................................................................................... -3 -4 -5 Fig. 15. As we approach x = 2 from the right, the y-values approach 4.

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