1. Let f(x) = { a sin ! r +0 i r= 0 i Is f(x) continuous at 0? Justify ii If f is discontinuous at 0, is the discontinuity removable or not? Justify iii If the discontinuity of f is removable, redefine f so that it's continuous at 0 iv Let f(x) = e-1/2² be defined on the domain {r : r+ 0}. - Find lim, 0 e-1/x², if it exists. Show that f can be defined at 0 in such a way that it is a continuous function on R v Let f(x) = sinļ, for # 0. Is f continuous at 0? Justify. Can f be defined at 0 so that it's continuous on R? Justify SO
1. Let f(x) = { a sin ! r +0 i r= 0 i Is f(x) continuous at 0? Justify ii If f is discontinuous at 0, is the discontinuity removable or not? Justify iii If the discontinuity of f is removable, redefine f so that it's continuous at 0 iv Let f(x) = e-1/2² be defined on the domain {r : r+ 0}. - Find lim, 0 e-1/x², if it exists. Show that f can be defined at 0 in such a way that it is a continuous function on R v Let f(x) = sinļ, for # 0. Is f continuous at 0? Justify. Can f be defined at 0 so that it's continuous on R? Justify SO
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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