Determine k, so thatis continuous at x = 6.

Question

Determine k, so that
$straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator straight x squared minus 36 over denominator straight x minus 6 end fraction comma space if space straight x not equal to 6 end cell row cell space space space space space space space straight k space space space space space space space comma space if space straight x equals 6 end cell end table close$
is continuous at x = 6.

Solution

straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator straight x squared minus 36 over denominator straight x minus 6 end fraction comma space if space straight x not equal to 6 end cell row cell space space space space space space space straight k space space space space space space space comma space if space straight x equals 6 end cell end table close space Lt with straight x rightwards arrow 6 straight x below straight f left parenthesis straight x right parenthesis equals Lt with straight x rightwards arrow 6 below fraction numerator straight x squared minus 36 over denominator straight x minus 6 end fraction space space space space space space space space space space space space space space space space equals Lt with straight x rightwards arrow 6 below fraction numerator left parenthesis straight x minus 6 right parenthesis left parenthesis straight x plus 6 right parenthesis over denominator straight x minus 6 end fraction equals Lt with straight x rightwards arrow 6 below left parenthesis straight x plus 6 right parenthesis equals 6 plus 6 equals 12 Since space straight f left parenthesis straight x right parenthesis space is space continous space at space straight x equals 6 therefore space space space space straight f left parenthesis 6 right parenthesis equals Lt with straight x rightwards arrow 6 below straight f left parenthesis straight x right parenthesis space space space space space space rightwards double arrow space straight k equals 12

For Daily Free Study Material Join wiredfaculty

Continuity And Differentiability

Some More Questions From Continuity and Differentiability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location