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Q.

Assertion (A): f(x) is continuous at x = a, if limxa⨍ (x) exists and equals to f(a).
Reason (R): If f(x) is continuous at a point, then1⨍ (x)  is also continuous at the point.

Assertion (A) and Reason (R). Answer these questions selecting the appropriate option given below:

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a

Both A and R are true and R is the correct explanation of A.

b

Both A and R are true and R is not the correct explanation of A.

c

A is true but R is false.

d

A is False but R is true.

answer is C.

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Detailed Solution

Assertion we know that If ⨍ (a)=limxa⨍ (x), then ⨍ (x) is continuous at x=a, while both hand must exist.   Reason If ⨍ (x) is continuous at a point, then it is not necessary that 1⨍ (x) is also continuous at that point. e.g.⨍ (x)=x is continuous at x=0 but ⨍ (x)=1x is not continuous at x=0.

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