MATH 203 Lecture Notes - Lecture 6: Product Rule
10 May 2016
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25: sin (a + b) = sin a cos b + sin b cos a cos (a + b) = cos a cos b (cid:0) sin a sin b. In right triangle (cid:1)oac : sin ]coa = = bd, arc(bc) = x; cos x = Areas: (cid:1)coa < (cid:1)cob < (cid:1)dob ! sin x cos x < x < tan x. 0 < lim x!0 x sin x x. 1 cos x (cid:21) 1 and lim x!0 cos x sin x x (cid:20) 1 ! 1 (cid:20) lim x!0 sin x x (cid:20) 1 ! lim x!0 sin x x. Ob = oc = 1; ]boc = x: (sin x)0. ; (cot x)0 sin (x + h) (cid:0) sin x (sin x)0 = lim h!0 h sin x cos (h) (cid:0) sin x lim h!0 h. = lim h!0 sin x cos (h) + cos x sin (h) (cid:0) sin x h. + lim h!0 cos x sin (h) h.
