HSC Commerce (Marketing and Salesmanship) 12th Board ExamMaharashtra State Board
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# Discuss Continuity of F(X) = X 3 − 64 √ X 2 + 9 − 5 for X≠4 = 10 for X = 4 at X = 4 - HSC Commerce (Marketing and Salesmanship) 12th Board Exam - Mathematics and Statistics

#### 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

2017-2018 (March) (with solutions)
Question 3.1.1 | 3.00 marks

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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.
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