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  • I need help with - Limit , continuity and differentiability - JEE Main-8

If f(x)= \sin x/x \forall x\neq 0 then the value of f(0) for which f(x) becomes continues at x= 0 will be 

  • Option 1)

    1

  • Option 2)

    2

  • Option 3)

    3

  • Option 4)

    no value

 

Answers (1)

best_answer

 As we have learned

Continuity at a point -

A function f(x)  is said to be continuous at  x = a in its domain if 

1.  f(a) is defined  : at  x = a.

2. \lim_{x\rightarrow a}\:f(x)\:exists\:means\:limit\:x\rightarrow a

of  f(x) at  x = a exists from left and right.

3. \lim_{x\rightarrow a}\:f(x)=f(a)\:then\:the\:limit\:equals \:the\:value\:at\:x=a

-

 

For continous at x= 0: \lim_{x\rightarrow 0}f(x)=f(0)

\therefore here \lim_{x\rightarrow 0}f(x)=\lim_{x\rightarrow 0}\frac{\sin x}{x}=1

f(0)=1 

 

 

 

 


Option 1)

1

Option 2)

2

Option 3)

3

Option 4)

no value

Posted by

Himanshu

View full answer

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