Question

funct (b) Use the graph of f(x) to answer the questions that follow: 10+ i. lim f(x) lim /(x) = lim f(x) = f(-2) - ii. Is f(x) continuous at -2? Explain briefly. $(2) = iii. lim (3) - lim f(x) = lim /(r) - iv. Is (1) continuous at : = 2? Explain briefly wolle v. List all intervals on which f(x) is continuous

Answer 1

(b)

From the graph,

(i)
lim fle I 3 ; as the function equals do 3 x-2- at - 2". 2 olim flow *+- 27 as flu approaches to - 2 at 113-2

um fou is not defined because for a function 1-2 to be continuous ata point, both Left hand timer and right hand limit should esust at the point hore, LH2= -3 and R42 = -2. So, lim H-2

3 is fl-2) = as it is clear from the graph that the bluedot in the graph at n=-2 corresponds to flw=-3.

(ii) at x = -2 , f(x) is not continuous because for f(x) to be continuous at x=-2 , its left hand limit and right hand limit must be equal at x = -2.

Here, LHL = -3 and RHL = -2 ,at the vicinity of x = -2 . So, f(x) is not continuous at the point.

Also, from the graph , the graph breaks at x = -2.

(iii)

fii 1 → um fil) = मन → lum flu) = hat defined M 2 > lim flow = -4 as LHL and RHL is not M2+ equal.

f(x) = ; because from the grapie the value et fin 2* H=2is__,
(iv)

At x = 2, f(x) is not continuous as for a function to be continuous it's left hand limit and right hand limit should be equal.But, from the graph, LHL = -1 and RHL = -4 which are not equal.

So, f(x) is not continuous at x = 2.

(v)

The interval in which f(x) is continuous is-

From the graph, graph, the interval in which fw is continuous is. at [-6,-2] u (-2,2) u [2,4) U[4,00)