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CBSE Class 12-science Answered

Find the value of k for which the function f(x) = open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell fraction numerator sin x over denominator x end fraction space plus space cos x space space i f space x equals divided by equals space 0 end cell blank row cell k space space space space space space space space space space space space space space space space space space space space space i f space space x space equals 0 end cell blank end table close is continuous at x=0
Asked by ahuja8087 | 14 Mar, 2017, 04:55: PM
answered-by-expert Expert Answer

begin mathsize 16px style It space is space given space that space the space function space straight f left parenthesis straight x right parenthesis space is space continuous space at space straight x equals 0. rightwards double arrow limit as straight x rightwards arrow 0 of straight f left parenthesis straight x right parenthesis equals straight f left parenthesis 0 right parenthesis rightwards double arrow limit as straight x rightwards arrow 0 of open parentheses sinx over straight x plus cosx close parentheses equals straight k rightwards double arrow limit as straight x rightwards arrow 0 of sinx over straight x plus limit as straight x rightwards arrow 0 of cosx equals straight k rightwards double arrow 1 plus 1 equals straight k space.... open square brackets Since space limit as straight x rightwards arrow 0 of sinx over straight x equals 1 close square brackets rightwards double arrow straight k equals 2 end style

Answered by | 14 Mar, 2017, 08:59: PM

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