A.

nπ 2 : n ∈ Z ( 2n+1 ( π 2 : n ∈ Z nπ : n ∈ Z 2nπ : n ∈ Z By Team Aakash Byju's | 19th December 2022

The correct answer is option B.

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[{"selector":"#anim-8509f84b-66d0-4d3d-b26b-b2ff9fd35d90","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-c2afa7d5-510f-4b14-808d-51f244a1b8d0","keyframes":{"transform":["translate3d(-1003.70342%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-b6bc4c8a-f382-460b-a4ed-24a857831064","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-129a4efd-7ead-4482-b8a9-f73f78aa7808","keyframes":{"transform":["translate3d(-1120.83382%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-ee5644dc-5c45-4612-a4a7-3cc54ce94a70","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-3af1be97-5bf6-404f-9e8c-58641d2b6d04","keyframes":{"transform":["translate3d(-774.28533%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-af94b387-b5f8-4fef-9800-58624c9c2fc3","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-bd1e4258-12f1-4f18-b272-d75a4bd0c962","keyframes":{"transform":["translate3d(-497.82607%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-edddd25b-43f1-432c-8e94-f17395f1fcbd","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-2632451e-7abb-4fea-a509-b3d6c6379f6e","keyframes":{"transform":["translate3d(-974.99985%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-aefa426b-f9f8-44eb-9534-e1bda9f714a5","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-e3d91a17-4a0a-4549-97e6-c55dff19dbd4","keyframes":{"transform":["rotate(-177deg) translate3d(-1169.99981%, 0px, 0) rotate(177deg)","rotate(-177deg) translate3d(0px, 0px, 0) rotate(177deg)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-11150bb0-a9d3-4c2a-ac85-fff2724ee3b8","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-c9bff705-0822-4070-b288-42d70c108a00","keyframes":{"transform":["translate3d(-914.99989%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] Detailed Explanation Arrow ( 2n+1 ( π 2 . . n ∈ Z

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We know that

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It is evident from the tan x graph that the value of tan x remains zero at ±π, ±2π, ±3π, so on. And it becomes ±∞ at ±π , ±3π , ±5π and so on.

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2

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2

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A.

The Function Given By f(x) = tan x Is Discontinuous on the Set

B.

C.

D.

{

{

{

{

{

{

{

{

The correct answer is option B.

{

{

We know that

lim tanx =∞ .

x

π

2

The graph of function tan x can be shown below.

It is evident from the tan x graph that the value of tan x remains zero at ±π, ±2π, ±3π, so on. And it becomes ±∞ at ±π , ±3π , ±5π and so on.

2

i.e., tan x = 0 for all x = nπ where n ∈ Z

tan x = ±∞ for all x =

(2n+1)π

2

where n ∈ Z.

2

Therefore, the function f(x) = tan x is discontinuous at

(2n+1)π

2

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