Ex 5.6, 9 - Find dy/dx, x = a sec, y = b tan - Chapter 5 CBSE - Ex 5.6

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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise

Transcript

Ex 5.6, 9 If x and y are connected parametrically by the equations without eliminating the parameter, Find ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ, ๐‘ฅ=๐‘Ž sec โก๐œƒ, ๐‘ฆ=๐‘ tanโก๐œƒ ๐‘ฅ=๐‘Ž sec โก๐œƒ, ๐‘ฆ=๐‘ tanโก๐œƒ ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ = ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ ร— ๐‘‘๐œƒ๏ทฎ๐‘‘๐œƒ๏ทฏ ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ = ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐œƒ๏ทฏ ร— ๐‘‘๐œƒ๏ทฎ๐‘‘๐‘ฅ๏ทฏ ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ = ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐œƒ๏ทฏ๏ทฎ ๐‘‘๐‘ฅ๏ทฎ๐‘‘๐œƒ๏ทฏ๏ทฏ Calculating ๐’…๐’š๏ทฎ๐’…๐œฝ๏ทฏ ๐‘ฆ = ๐‘ tan๏ทฎ๐œƒ๏ทฏ ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐œƒ๏ทฏ = ๐‘‘ ๐‘ tan๏ทฎ๐œƒ๏ทฏ๏ทฏ๏ทฎ๐‘‘๐œƒ๏ทฏ ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐œƒ๏ทฏ = ๐‘ ๐‘‘ tan๏ทฎ๐œƒ๏ทฏ๏ทฏ๏ทฎ๐‘‘๐œƒ๏ทฏ ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐œƒ๏ทฏ = ๐‘ . sec๏ทฎ2๏ทฏ๏ทฎ๐œƒ๏ทฏ ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ = ๐‘ . 1๏ทฎ cos๏ทฎ๐œƒ๏ทฏ๏ทฏ๏ทฎ๐‘Ž sin๏ทฎ๐œƒ๏ทฏ๏ทฎ cos๏ทฎ๐œƒ๏ทฏ๏ทฏ๏ทฏ๏ทฏ ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ = ๐‘ ร— 1๏ทฎ cos๏ทฎ๐œƒ๏ทฏ๏ทฏ ร— cos๏ทฎ๐œƒ๏ทฏ๏ทฎ a sin๏ทฎ๐œƒ๏ทฏ๏ทฏ ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ = ๐‘๏ทฎ๐‘Ž๏ทฏ 1๏ทฎ sin๏ทฎ๐œƒ๏ทฏ๏ทฏ๏ทฏ ๐’…๐’š๏ทฎ๐’…๐’™๏ทฏ = ๐’ƒ๏ทฎ๐’‚๏ทฏ ๐’„๐’๐’”๐’†๐’„ ๐œฝ

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