T h e space f u n c t i o n space g space g i v e n space b y g left parenthesis

Question

T h e space f u n c t i o n space g space g i v e n space b y g left parenthesis x right parenthesis space equal space fraction numerator cos left parenthesis x right parenthesis over denominator 3 x end fraction i s space n o t space d e f i n e d space f o r space x equal 0 space s o space i s space n o t space c o n t i n u o u s space a t space x equal 0. W e space w u s h space t o space a s s i g n space a space v a l u e space t o space g left parenthesis 0 right parenthesis space s o space t h e space r e s u l t i n g space f u n c t i o n space i s space c o n t i n u o u s space a t space x equal 0. space space T h e space v a l u e space f o r space g left parenthesis 0 right parenthesis space i s The function g given by g(x)= cos(x)/3x is not defined for x=0 so is not continuous at x=0. We wish to assign a value to g(0) so the esulting function is continuous at x=0. The value for g(0) is?

Explanation / Answer

lim x tends to 0 sin x/3x=1/3

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