Chapter 8 Continuity Miscellaneous Exercise 8 Solutions

Maharashtra State Board 11th Maths Solutions Chapter 8 Continuity Miscellaneous Exercise 8

(I) Select the correct answer from the given alternatives.

II. Discuss the continuity of the following functions at the point(s) or on the interval indicated against them.

(ii) 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).

(iii) For 4 ≤ x ≤ 7, x ≤ 5
f(x) =
It is a rational function and is continuous everywhere except at points where its denominator becomes zero.
Denominator becomes zero at x = 5
But x = 5 does not lie in the interval.
∴ f(x) is continuous at all points in (4, 7] – {5}.

(iv) For continuity at x = 2:

∴ f(x) is continuous at x = 2.

(v) For continuity at x = 4:

∴ f(x) is continuous at x = 4.

(vi) For continuity at x = 5.
f(5) = 7

∴ f(x) is discontinuous at x = 5.
Thus, f(x) is continuous at all points on its domain except at x = 5.

(ii) For continuity at x = 0:


∴
∴ f(x) is discontinuous at x = 0.

III. Identify discontinuities if any for the following functions as either a jump or a removable discontinuity on their respective domains.

IV. Discuss the continuity of the following functions at the point or on the interval indicated against them. If the function is discontinuous, identify the type of discontinuity and state whether the discontinuity is removable. If it has a removable discontinuity, redefine the function so that it becomes continuous.

V. Find k if the following functions are continuous at the points indicated against them.

VI. Find a and b if the following functions are continuous at the points or on the interval indicated against them.

VII. Find f(a), if f is continuous at x = a where,

VIII. Solve using intermediate value theorem.