Question

to find analytically the limit of a function f(x) at x=c and also check the continuity of the function at that point

Answer 1

Step-by-step explanation:

Finding analytically the limit of a function f(x) at x=a and hence verifying the continuity of the function at that point.

Answer 2

The limit of a function is a number that a function reaches when its independent variable reaches a given value.

• The value (say a) to which the function f(x) approaches as the value of the independent variable x arbitrarily approaches a given value "A," symbolised as f(x) = A.
• A function is said to be continuous at a given point if there is no break in its graph at that point. First, a function f with variable x is continuous at the real line point "a" if the limit of f(x) as x approaches the point "a" is equal to the value of f(x) at "a," i.e., f (a). Second, the function (as a whole) is continuous, if it is continuous at every point in its domain.
• For example: let the function is $\lim_{x \to \(-2} 3x^{2} +5x-9$

        $\lim_{x \to \(-2^{-} } = \lim_{x \to \(-2^{+} } =6x+5$

        $6(-2) + 5$

        $-7$

• So, the function is continuous at x = -2 and the limit of the function is -7.

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