Continuity

Ex. No. 3.1

1. Are the following functions continuous on the set of real numbers? Justify your answers: [Solution & Video Click Here]


(i) f(x) = 7

(ii) f(x) = e

(iii) f(x)  = log 19

(iv) f(x) = 7x4 - 5x3 - 3x + 1

(v) g(x) = sin(4x - 3)

(vi) h(x) = (5x2 + 7x + 2) / x3 + x2 + x + 3

vii. g(x) = 13x2 + 16x + 19

viii. f(x) = 5x

ix. f(x) = 32x - 15x

x. f(x) = e5x+7


2. Examine the continuity of the following functions at the given points:


(i) f(x) = x2  - x + 9 for x ≤ 3

= 4x + 3 for x > 3 at x = 3 [Solution & Video Click Here]


(ii)  f(x) = x2 - 16 / 4 - 4 for x =/ 4 [Solution & Video Click Here]