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File0037

# File0037 - 120 M 15 16 17 18 19 20 21 22 23 24 25 26 27...

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Unformatted text preview: 120 M 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. Chapter 3 Differentiation S _ l+Csct : g _ (l —esc I)(—csc tcott)—(1 +CsC t)(csctcot t) — l—csct dt— (l—Csct) _,_ vcsctcotllecscztcoltiesctcotticscztcott _ —2 csctcott "2 (l —csc t) _ (l —csc 07 s , sint : g , (I —cosIXCOSO—(sinmsint) __ cost~c052t—sm2t _ cost—l _ _ 1 _ l—cost dt ‘4' 0—90le .. (1—C0h[)2 _ (l—cusl)E - l—cost I _ cost-l r= 4— 02 sin0 => g; = — (02 f—Msin 6)+ (sin 0)(20)) : —(02 c080+20 sin 0) : —0(6 cosﬂ+25in 0) r=65in6+c056 => :7;=(600s6+(sin0)(l))—sin0=00050 r 2 sec 9 csc 6 => 3% = (sec t9)(~csc 6 cot 0) + (030 9)(sec 0 tan 0) = (“1%)(st—\$5)(§?:3)+(ﬁ)(ﬁ)(§\$%) = ‘—19 + c—nirs = \$6029 - 68629 r: (l + see 6)sin0 => 5—;- = (1 +sec 0)Cos9+(sin 9)(sec0tan6) : (c056+1)+tan20 = cosﬁ+sec20 p:5+L=5+tanq -—-> gg=sec2q p = (l +csc q)cosq => 35 = (l +csc q)(~sin q) + (cos q)(icscqcot q) = (—sin q — l) — cotzq = ——sin q ~ csczq _ sin 9 + cos 9 Z) 512 _ (cos g)(cus g A sin 9) 7 (sin 9 +cos g)(—sin g) p '_ cos q dq _ cos2 (.1 2 . .- - 2 ' _cosq—cosgsmg+sm q+gsgsmq _ 1 _ 2 _ cos q _ coszq _ SEC q 7 tang c_lp _ (1+lanq) seCQQ)-(tan (.1)(sec2 q) _ sec2 +tan sec2 -tan sec2 _ 3602 p — l+tanq : dq — (1+lanq) — (Hmnq)é — (l+tanq)§ a) = 050 x :> ’ = —CSC x cot x :> ” = — (:30 x) —cs<:2 x + (cot x)(—csc X cot x) = CSC3 x + CSC x cot2x y y y : (csc x) (csc2 x + cot2 x) : (csc x) (0ch x + csc2 x — l) = 2 csc3 x — csc x (b) y 2 sec x => 3" = sec x tan x 2> y” = (scc x) (sec2 x) + (tan x)(sec x tan x) : sec3 x + sec x tan2 x 2 (sec x) (sec2 x + tan2 x) 2 (sec x) (sec2 x + see2 x — l) 2 2 sec3 x — sec x (a) y2725inx—>y’~ 2cosx—>y”= 2( sinx) 23inx >y’” 2cosx 1y“) 2sinx (b) y=9cosx => y’:—9sinx —> y"— 9c0sx —> y'”— 9( sinx).—9sinx —> y(4)—9cosx y : sin x :> y’ : cos x => slope 0ftangent at x = in is y’(~7r) = cos(i7r) = 71; slope of tangent at x = O is y’(0) : cos (0) = l; and slope of tangent at x z 3.7" is y’ (3—271) 2 cos 321 = 0. The tangent at (—71', O) is y — 0 : —1(x + 7r), or y 2 —x — 71'; the tangent at (0,0) is y ~ 0 : 1(x — 0), ory : x; and the tangent at (921,7 )isy: ~71. ...
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