#### Question

Discuss continuity of f(x) =`x^3-64/(sqrtx^2+9-5)`For x≠4

= 10 for x = 4 at x = 4

#### Solution

`Lim_(x→4)x^3-64/(sqrtx^2+9-5)`

`Lim_(x→4)x^3-64/(sqrtx^2+9-5)`

`Lim_(x→4)(x^3-64)/(sqrtx^2+9-5)xx(sqrtx^2+9+5)/(sqrtx^2+9+5)`

`Lim_(x→4)((x^3-64)(sqrtx^2+9+5))/((sqrtx^2+9)^2-(-5)^2)`

`Lim_(x→4) ((x-4)(x^2+4x+16)(sqrtx^2+9+5))/(x^2+9-25)`

`[a^3 – b^3 = (a – b) (a^2 + ab + b^2))`

`Lim_(x→4) ((x-4)(x^2+4x+16)(sqrtx^2+9+5))/(x^2-16)`

`Lim_(x→4) ((x-4)(x^2+4x+16)(x^2+9+5))/((x-4)(x+4)`)

`Lim_(x→4) ((x+4x+16)(sqrtx^2+9+5))/(x+4)`

`({(4)^2+4(4)+16}(sqrt4^2+9+5))/(4+4)`

`((16+16+16)(5+5))/8`

`f(x)lim_(x→4)=60`

`Lim_(x→4) f(x)≠f(4)`

∴ f (x) is not continuous at x = 4.

Is there an error in this question or solution?

#### APPEARS IN

Solution Discuss Continuity of F(X) = X 3 − 64 √ X 2 + 9 − 5 for X≠4 = 10 for X = 4 at X = 4 Concept: Continuous Function of Point.