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summary of this topic

Basics: Limit of a function

Basics: Limit of a function

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Limit of a Function


 »  If both left-hand-limit and right-hand-limit are equal, it is together referred as "limit of the function"

Limit of a function

plain and simple summary

nub

plain and simple summary

nub

dummy

When left-hand-limit and right-hand-limit are equal, the limits are referred together as limit of a function.

simple steps to build the foundation

trek

simple steps to build the foundation

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The right-hand and left-hand limits are equal for most input values for most functions. This is commonly referred as limit of a function.


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Starting on learning "limit of a function". ;; The right-hand and left-hand limits are equal for most input values for most functions. This is commonly referred as limit of a function.

Given that function `f(x)` evaluates to indeterminate value at `x=a`. To evaluate the expected value of `f(x)|_(x=a)`, we examine ;

 •  Left-hand-limit `lim_(x->a-) f(x)`

 •  Right-hand-limit `lim_(x->a+) f(x)`

If these two limits are equal then the result is referred as "limit of the function at the input value" `lim_(x->a) f(x)`

The significance of this is that, most functions have both right-hand-limit and left-hand-limit equal.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Limit of a function: Given function `f(x)` and that `f(x)|_(x=a) = 0/0`.
If `lim_(x->a+) f(x) = lim_(x->a-) f(x)`,
then the common value is referred as limit of the function `lim_(x->a) f(x)`.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

If a function `f(x)` is discontinuous at `x=a`, then what is `lim_(x->a) f(x)`?

  • left-hand-limit
  • right-hand-limit
  • `f(a)`
  • cannot be computed

The answer is 'cannot be computed'. It is given that the function is discontinuous at `x=a`, and that implies left-hand-limit and right-hand-limits are not equal. In that case, limit of the function cannot be computed without specifying left or right.

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Given that function f of x evaluates to indeterminate value at x=a. To evaluate the expected value of f of x at x=a, we examine ;; Left-hand-limit limit x tending to a. minus f of x ;; Right-hand-limit limit x tending to a. plus f of x ;; If these two limits are equal then the result is referred as "limit of the function at the input value" limit x tending to a. f of x ;; The significance of this is that, most functions have both right-hand-limit and left-hand-limit equal.
When left-hand-limit and right-hand-limit are equal, the limits are referred together as limit of a function
Limit of a function: Given function f of x and that f of x at x=a equals 0 by 0.;; If limit x tending to a. plus f of x equals limit x tending to a. minus f of x ;; then the common value is referred as limit of the function limit x tending to a. f of x.
If a function f of x is discontinuous at x=a, then what is limit x tending to a. f of x?
left
left-hand-limit
right
right-hand-limit
f;a
f of a
cannot;computed
cannot be computed
The answer is 'cannot be computed'. It is given that the function is discontinuous at x=a , and that implies left-hand-limit and right-hand-limits are not equal. In that case, limit of the function cannot be computed without specifying left or right.

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