# barry tan - Microsoftu00ae Word 2019_000167.pdf - a 1...

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a.1; because as x approaches 0 from left or right side, the curve approaches the y-value of 1. b.Does not exist; because sine curve is an oscillating curve and the limit is impossible to determine. a.5?4cos(?5)b.5?𝑖?4?????c.−4sin (4? + 9)d.−2??𝑖?(2?2+ 6)e.2??𝑖?(?2+ 5) + 2?3cos (?2+ 5)f.5??g.?5?5
h.?3?+1+ 3?3?+1?i.1?+3j.10??2+4k.5???(5)l.4?(?2+ 2)(?2+ 2? + 1)3+ 3(?2+ 2? + 1)2(2? + 2)(?2+ 2)2m.cot (?)n.5(? + ln (?))4(1 +1?)ln(?) = ln ((?+3)2(?+2)5(?+4)7)ln(?) = ln(? + 3)2− ln((? + 2)5(? + 4)7)ln(?) = 2ln(? + 3) − (ln((? + 2)5) + ln((? + 4)7))ln(?) = 2ln(? + 3) − (5 ln(x + 2) + 7 ln(x + 4))ln(?) = 2ln(? + 3) − 5 ln(x + 2) − 7ln (? + 4)1??=2?+35?+27?+41??=−10?2−58?−86(?+3)(?+2)(?+4)1??=−10?2−58?−86(?+3)(?+2)(?+4)??= (−10?2−58?−86(?+3)(?+2)(?+4)) ((?+3)2(?+2)5(?+4)7)?=−2(5?2+29?+43)(?+3)(?+2)6(?+4)8
?=2??2−2? =2(3)(3)2−2? =67? = ln(32− 2)? ≈ 1.945910149? = ?(? − ?1) + ?1? =67(? − 3) + 1.945910149? =67? −187+ 1.945910149? =67? −187+ 1.945910149? =67? − 0.626?= −2 cos ? sin ?? = −2 cos𝜋3sin𝜋3? = −√32? = ???2(𝜋3)? =14? = ?(? − ?1) + ?1? = −√32(? −𝜋3) +14? = −√32? +√3𝜋6+14? = −√??? +√?𝝅?+??Therefore, the equation of the tangent line to the function is approximately ? =??? − ?. ???Therefore, the equation of the tangent to the curve is ? = −√??