NED University of Engineering & Technology, Karachi*
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MATH 1342
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Feb 11, 2024
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2(cz)* +x -1 forzx<1 2cx + (r—1)> forz > 1 (b) f(z)= { 3z+c¢ forz< -1 () f(x)=¢ 22—c for —1<x<2 3 forz>2 5.% Consider the function f(x) = |z], the greatest integer function (also called the floor function or the step function). Where is this function discontinuous? 6.* Find an example of a function such that the limit exists at every x, but that has an infinite number of discontinuities. (You can describe the function and/or write a formula down and/or draw a graph.) PARTIAL ANSWERS: 1. (a)z=0,3 (b)z=-2,0,1 2. (a) R (b) R\{-1/2,2} (c) (—o00,5] (d) (-3,2)U(-2,2)U(2,4) 3. (a) discontinuous only at x =1 (b) discontinuous only at z = 2 4. (a)e=8 (b)e=-1,0,1 (c) no solution possible 5. discontinuous at every integer, r = ...,—-3,-2,-1,0,1,2,3,... 6. many answers are possible, show me your solution!
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