438
Chapter 4 | Applications of Derivatives
2 + x −2 x 2 −3 x −4
298. y = x
299. y = x 2 −5 x +4 300. y =2 x 16− x 2 301. y = cos x
x , on x = [−2 π , 2 π ]
302. y = e x − x 3 303. y = x tan x , x = [− π , π ] 304. y = x ln( x ), x >0 305. y = x 2 sin( x ), x = [−2 π , 2 π ]
P ( x ) Q ( x )
306. For f ( x ) = to have an asymptote at y =2 then the polynomials P ( x ) and Q ( x ) must have what relation? 307. For f ( x ) = to have an asymptote at x =0, then the polynomials P ( x ) and Q ( x ). must have what relation? 308. If f ′( x ) has asymptotes at y =3 and x =1, then f ( x ) has what asymptotes? P ( x ) Q ( x )
309. Both f ( x ) = 1
and g ( x ) = 1
have
( x −1)
( x −1) 2
asymptotes at x =1 and y =0. What is the most obvious difference between these two functions? 310. True or false: Every ratio of polynomials has vertical asymptotes.
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