examine the continuity of the function f(x)=x square +5 at x=1

Asked by Rashmi gondi | 21st Dec, 2013, 06:58: PM

Expert Answer:

The function is continuous at x=1 if it is defiined at x=1.
Also the LHL f(x) at x=1 = RHL of f(x) at x= 1 = f(1) if f is continuous at x=1.
 
Now let us find the left hand limit:
 
Similarly, let us find the right hand limit of the given function:
 
 
And we have,
Since the right hand limit, left hand limit and f(1) are equal to 6 and it is finite, the function
 
is continuous at x = 1

Answered by Vimala Ramamurthy | 22nd Dec, 2013, 02:25: PM

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