For each of the following triangles, solve for B and use the results to explain why the and triangle has the given number of solutions.A = 30, b = 40 ft, alOft; no solution

MTH 132 Lecture 5 Continuity Recap of Continuity ● We studied the limit x → a f(x) and the limit x→a±. ● Definition: f(x) is continuous at x = a, if and only if lim x→a f(x) = f(a) 1. Limit exists. 2. f(a) = defined. 3. f(x) = f(a) ● At a = 1 limit = 1 ≠ f(1) not continuous at 1. ● At a = 2 limit = 0 ≠ f(2) not continuous at 0. ● At a = 3 limit = DNE ≠ f(3) not continuous at f(3) ● Example: ○ xsin1/x ○ f(x) isn’t continuous at x = 0 since f(0) is not defined. ○ Limit x → 0 f(x) ○ − |x| ≤ f(x) ≤ |x| ○ Both |x| and |x| = 0, meaning that 0 is a removab