2 =x1 using (b) =x Identity laws x(xy) = xxxy Distributivity laws =xxy by (a) =x Just shown above QED Definition An element y in B is called a complement of an element x in B if xTo get a better idea of what the limit is, we need to factor the denominator lim x → 2 − x − 3 x2 − 2x = lim x → 2 − x − 3 x(x − 2) Step 2 Since x − 2 is the only part of the denominator that is zero when 2 is substituted, we then separate 1/(x − 2) from the rest of the function = lim x → 2 − x − 3 x 1 xLet's use these laws to calculate the limits in a couple examples Example 1 Evaluate the following limit and justify each step Step 1 Apply the Product of Limits Law 4 Step 2 Apply the Difference and Sum of Limit Laws 2 & 1 Step 3 Apply the Constant Multiple Law 3 Step 4 Apply Limit Law 9
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