Balbharati Maharashtra State Board11th Commerce Maths Solution Book PdfChapter 8 Continuity Miscellaneous Exercise 8 Questions and Answers.
Maharashtra State Board 11th Commerce Maths Solutions Chapter 8 Continuity Miscellaneous Exercise 8
I. Discuss the continuity of the following functions at the point(s) or in the interval indicated against them.
b. For 2 < x < 4
f(x) =
It is a rational function and is continuous everwhere except at points where its denominator becomes zero.
Denominator becomes zero at x = 1
But x = 1 does not lie in the interval.
f(x) is continuous at all points in (2, 4)
c. For 4 < x ≤ 7, x ≠ 5
i.e. for x ∈ [4, 5) ∪ (5, 7]
∴ f(x) =
It is a rational function and is continuous everywhere except possibly at points where its denominator becomes zero.
Denominator becomes zero at x = 5
But x = 5 ∉ [4, 5) ∪ (5, 7]
∴ f is continuous at all points in (4, 7] – {5}.
d. Since the definition of function changes around x = 2, x = 4 and x = 7
∴ there is disturbance in behaviour of the function.
So we examine continuity at x = 2, 4, 7 separately.
Continuity at x = 2:
= 2(2)2– 2(2) + 5
= 8 – 4 + 5
= 9
∴ f is continuous at x = 2
e. Continuity at x = 4:
∴ f is continuous at x = 4
(II) Find k if following functions are continuous at the points indicated against them.
III. Find a and b if following functions are continuous at the point indicated against them.
