#### Chapters

## Chapter 8: Continuity

### Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board Chapter 8 Continuity Exercise 8.1 [Pages 111 - 112]

Examine the continuity of f(x) = x^{3} + 2x^{2} − x − 2 at x = –2.

Examine the continuity of f(x) = `(x^2 - 9)/(x - 3)` on R.

Examine whether the function is continuous at the points indicated against them:

f(x) = x^{3} − 2x + 1, for x ≤ 2

= 3x − 2, for x > 2, at x = 2

Examine whether the function is continuous at the points indicated against them:

f(x) = `(x^2 + 18x - 19)/(x - 1)` for x ≠ 1

= 20 for x = 1, at x = 1

Test the continuity of the following function at the points indicated against them:

`f(x) = (sqrt(x - 1) - (x - 1)^(1/3))/(x - 2)` for x ≠ 2

= `1/5` for x = 2, at x = 2

Test the continuity of the following function at the points indicated against them:

`"f"(x) = (x^3 - 8)/(sqrt(x + 2) - sqrt(3x - 2))` for x ≠ 2

= – 24 for x = 2, at x = 2

Test the continuity of the following function at the points indicated against them:

f(x) = 4x + 1, for x ≤ 3

= `(59 - 9x)/3`, for x > 3 at x = `8/3`.

Test the continuity of the following function at the points indicated against them:

f(x) = `(x^3 - 27)/(x^2 - 9)` for 0 ≤ x <3

= `9/2` for 3 ≤ x ≤ 6, at x = 3

If `f(x) = (24^x - 8^x - 3^x + 1)/(12^x - 4^x - 3^x + 1)` for x ≠ 0

= k, for x = 0

is continuous at x = 0, find k.

If `f(x) = (5^x + 5^-x - 2)/(x^2)` for x ≠ 0

= k for x = 0

is continuous at x = 0, find k

For what values of a and b is the function

f(x) = ax + 2b + 18 for x ≤ 0

= x^{2} + 3a − b for 0 < x ≤ 2

= 8x – 2 for x > 2,

continuous for every x ?

For what values of a and b is the function

`f(x) = (x^2 - 4)/(x - 2)` for x < 2

= ax^{2} − bx + 3 for 2 ≤ x < 3

= 2x – a + b for x ≥ 3

continuous in its domain.

### Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board Chapter 8 Continuity Miscellaneous Exercise 8 [Page 113]

Discuss the continuity of the following function at the point(s) or in the interval indicated against them:

f(x) = 2x^{2} − 2x + 5 for 0 ≤ x < 2

= `(1 - 3x - x^2)/(1 - x)` for 2 ≤ x < 4

= `(7 - x^2)/(x - 5)` for 4 ≤ x ≤ 7 on its domain.

Discuss the continuity of the following function at the point(s) or in the interval indicated against them.

`f(x) = (3^x + 3^-x - 2)/x^2` for x ≠ 0.

= (log3)^{2} for x = 0 at x = 0

Discuss the continuity of the following function at the point(s) or in the interval indicated against them:

`f(x) = (5^x - e^x)/(2x)` for x ≠ 0

= `1/2`(log5−1) for x = 0 at x = 0

f(x) = `(sqrt(x + 3) - 2)/(x^3 - 1)` for x ≠ 1

= 2 for x = 1, at x = 1.

`f(x) = (log x - log 3)/(x - 3)` for x ≠ 3

= 3 for x = 3, at x = 3.

Find k if the following function is continuous at the points indicated against them:

`f(x) = ((5x - 8)/(8 - 3x))^(3/(2x - 4)` for x ≠ 2

= k for x = 2 at x = 2.

Find k if the following function is continuous at the points indicated against them:

`f(x) = (45^x - 9^x - 5^x + 1)/((k^x - 1)(3^x - 1))` for x ≠ 0

= `2/3` for x = 0, at x = 0

Find k if the following function is continuous at the points indicated against them:

`f(x) = (1 + kx)^(1/x)` , for x ≠ 0

= `e^(3/2)` , for x = 0, at x = 0

Find a and b if the following function is continuous at the point indicated against them.

`f(x) = x^2 + a` , for x ≥ 0

= `2sqrt(x^2 + 1) + b` , for x < 0 and

f(1) = 2 is continuous at x = 0

Find a and b if the following function is continuous at the point indicated against them.

`f(x) = (x^2 - 9)/(x - 3) + "a"` , for x > 3

= 5 , x = 3

= 2x^{2} + 3x + b , for x < 3

is continuous at x = 3

Find a and b if the following function is continuous at the point indicated against them.

`f(x) = (32^x - 1)/(8^x - 1) + a` , for x > 0

= 2 , for x = 0

= x + 5 − 2b , for x < 0

is continuous at x = 0

## Chapter 8: Continuity

## Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board chapter 8 - Continuity

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board chapter 8 (Continuity) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board chapter 8 Continuity are Continuous and Discontinuous Functions, Continuity of a Function at a Point, Definition of Continuity, Continuity from the Right and from the Left, Properties of Continuous Functions, Continuity in the Domain of the Function, Examples of Continuous Functions Whereever They Are Defined.

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