Archive
14th of March 2017
Mathematics
Q:

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 closeis continuous at x=0

Ahuja8087 Ahuja - CBSE - Class XII Science

Tuesday, March 14, 2017 at 16:55:PM

A:

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

Tuesday, March 14, 2017 at 20:59:PM