Get live Maths 1-on-1 Classs - Class 6 to 12

Ex 13.1

Ex 13.1, 1

Ex 13.1, 2

Ex 13.1, 3

Ex 13.1, 4 Important

Ex 13.1, 5

Ex 13.1, 6 Important

Ex 13.1, 7

Ex 13.1, 8 Important

Ex 13.1, 9

Ex 13.1,10 Important

Ex 13.1, 11

Ex 13.1, 12

Ex 13.1, 13

Ex 13.1, 14 Important

Ex 13.1, 15 Important

Ex 13.1, 16

Ex 13.1, 17 Important

Ex 13.1, 18

Ex 13.1, 19 Important

Ex 13.1, 20

Ex 13.1, 21 Important

Ex 13.1, 22 Important You are here

Ex 13.1, 23

Ex 13.1, 24

Ex 13.1, 25 Important

Ex 13.1, 26

Ex 13.1, 27

Ex 13.1, 28 Important

Ex 13.1, 29

Ex 13.1, 30 Important

Ex 13.1, 31

Ex 13.1, 32 Important

Last updated at March 16, 2023 by Teachoo

Ex 13.1, 22 lim┬(x → π/2) tan2x/(x − π/2) lim┬(x → π/2) tan2x/(x − π/2) Putting y = x – π/2 When x → 𝜋/2 y → 𝜋/2 – 𝜋/2 y → 0 So, our equation becomes lim┬(x→π/2) tan2x/(x − π/2) = lim┬(y→0) (tan2(𝜋/2 + 𝑦)/𝑦) = lim┬(y→0) ((〖tan 〗〖(𝜋 + 2𝑦〗))/𝑦) = lim┬(y→0) (tan2𝑦/𝑦) = lim┬(y→0) (1/𝑦 . sin2𝑦/cos2𝑦 ) = lim┬(y→0) (sin2𝑦/𝑦 . 1/cos2𝑦 ) = lim┬(y→0) sin2𝑦/𝑦 ×lim┬(y→0) 1/cos2𝑦 Multiply & Divide by 2 (As tan〖(𝜋+𝑥〗)=tan x) = lim┬(y→0) (sin2𝑦/𝑦 "× " 2/2).lim┬(y→0) 1/cos2𝑦 = 2 lim┬(y→0) (𝒔𝒊𝒏𝟐𝒚/𝟐𝒚).lim┬(y→0) 1/cos2𝑦 Using ( lim)┬(x→0) (sinx )/x = 1 Replacing x by 2y. lim┬(x→0) sin2𝑦/2y = 1 = 2 × 1 × lim┬(y→0) 1/cos2𝑦 = 2 × 1/cos〖2(0)〗 = 2/cos0 = 2/1 = 2 (As cos 0 = 1)