A function f(x) is defined as ,

f(x)={(x²-x-6)/x-3; if x not =3

5 ;if x=3.

Show that f(x) is continuous at x=3.

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A function f(x) is defined as ,
f(x)={(x2-x-6)/x-3; if x not =3
5 ;if x=3
Show that f(x) is continuous at x=3

Manbar Singh · Accepted Answer

It is given that : f x = x2 - x - 6x - 3, if x ≠ 0 5, if x =
3 We have to show that f x is continuous L H L at x =
3limx→3- f x = limx→3- x2 - x - 6x - 3 = limx→3-
x - 3 x + 2x - 3 = limx→3- x + 2limh→0 3 -h + 2 put x =
3 - h as x→3 then, h→0limh→0 5 - h = 5R H L at x
= 3limx→3+ f x = limx→3+ x2 - x - 6x - 3 =
limx→3+ x - 3 x + 2x - 3 = limx→3+ x + 2limh→0 3
+ h + 2 put x = 3 + h as x→3 then, h→0limh→0 5 +
h = 5f 3 = 5Since limx→3- fx = limx→3+ fx = f 3Hence,
the function is continuous at x = 3

A function f(x) is defined as , f(x)={(x2-x-6)/x-3; if x not =3 5 ;if x=3. Show that f(x) is continuous at x=3.

A function f(x) is defined as ,

f(x)={(x²-x-6)/x-3; if x not =3

5 ;if x=3.

Show that f(x) is continuous at x=3.