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Continuity is considered one of the most asked concept.
293 Questions around this concept.
In which of the following,
If the function.
is differentiable, then the value of
Consider the function.
where
f(x) is said to be continuous in (a,b) if it is continuous of -------------- point of the interval (a,b)
Match the following
(i)
(p) Limit exists at
(ii)
(q) Continuous at
(iii)
(r) Limit doesn't exist at
The function
Let
If
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If
The function f(x) is said to be continuous from left at x=a if
Find the points of continuity but non-differentiability in the graph below:
Continuity
Many functions have the property that their graphs can be traced with a pen/pencil without lifting the pen/pencil from the page. Such functions are called continuous. Other functions have points at which a break in the graph occurs, but satisfy this property over some intervals contained in their domains. They are continuous on these intervals and are said to have a discontinuity at a point where a break occurs. So continuity can be defined in two ways: Continuity at a point and Continuity over an interval.
Continuity at a point
Let us see different types of conditions to see continuity at point
We see that the graph of
(i)
Next, for the graph given below, although
(ii)
The above two conditions by themselves do not guarantee continuity at a point. The function in the figure given below satisfies both of our first two conditions but is still not continuous at a. We must add a third condition to our list:
(iii)
So, a function
1.
2.
3.
Or
i.e. L.H.L.
A function is discontinuous at a point a if it fails to be continuous at a.
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