Ex 13.1

Chapter 13 Class 11 Limits and Derivatives
Serial order wise

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### Transcript

Ex 13.1, 17 Evaluate the Given limit: lim┬(x→0) cos⁡〖2x − 1〗/cos⁡〖x − 1〗 lim┬(x→0) ( 𝐜𝐨𝐬⁡〖𝟐𝐱 〗− 1)/cos⁡〖x − 1〗 = lim┬(x→0) ((𝟏 − 𝟐 〖𝐬𝐢𝐧^𝟐〗⁡𝒙) − 1)/cos⁡〖𝑥 − 1〗 = lim┬(x→0) (1 − 2 〖𝐬𝐢𝐧^𝟐〗⁡𝒙 − 1 )/cos⁡〖x − 1〗 = lim┬(x→0) (−2 𝐬𝐢𝐧𝟐 𝐱 )/cos⁡〖x − 1〗 = lim┬(x→0) (−2(𝟏 − 𝐜𝐨𝐬^𝟐 𝒙))/cos⁡〖x − 1〗 = lim┬(x→0) (−2(1 − 𝐜𝐨𝐬^𝟐 𝒙) )/(−1(1−〖 cos〗⁡〖𝑥)〗 ) (Using cos 2x = 1 – 2sin2 x) (Using sin2 x = 1 – cos2 x ) = lim┬(x→0) ( 2 (12 − cos2 x) )/( 1−〖 cos〗⁡𝑥 ) = lim┬(x→0) ( 2 (1 − cos x)(1 +〖 cos〗⁡〖𝑥)〗 )/( 1−〖 cos〗⁡𝑥 ) = lim┬(x→0) 2 (1 + cos x) Putting x = 0 = 2 (1 + cos 0) = 2 (1 + 1) = 2 × 2 = 4

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.