Question

Discuss the continuity of the function f given by
$straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 2 plus straight x space comma space if space straight x not equal to 0 end cell row cell space space space space space 2 space space comma space if space straight x equals 0 end cell end table close at space straight x equals 0$

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Solution

We space have space straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 2 plus straight x space comma space if space straight x not equal to 0 end cell row cell space space space space space 2 space space comma space if space straight x equals 0 end cell end table close space Lt with straight x rightwards arrow 0 to the power of minus below straight f left parenthesis straight x right parenthesis equals Lt with straight x rightwards arrow 0 to the power of minus below left parenthesis 2 plus straight x right parenthesis equals 2 space Lt with straight x rightwards arrow 0 to the power of plus below straight f left parenthesis straight x right parenthesis equals Lt with straight x rightwards arrow 0 to the power of plus below left parenthesis 2 plus straight x right parenthesis equals 2 Also space straight f left parenthesis 0 right parenthesis equals 2 therefore space Lt with straight x rightwards arrow 0 to the power of minus below straight f left parenthesis straight x right parenthesis equals Lt with straight x rightwards arrow 0 to the power of plus below straight f left parenthesis straight x right parenthesis equals straight f left parenthesis 0 right parenthesis

∴ f is continuous at x = 0.

For Daily Free Study Material Join wiredfaculty