REFERENCE page 4 SPECIAL FUNCTIONS Exponential and Logarithmic Functions ogbx=y→b'=x =e Inx log,x.where In e=1 nx-y→e'-x =hx Cancellation Equations Laws of Logarithms logs(b")-x bl=x 1.loga(xy)=logox logsy In(e")=x =x 2e(月）-gr-y lim e=0 lim e'-o 3.log(x)=rlogs limg,Inx =-%0 lim Inx=x /2 y=log,x 15 0号5 Exponential functions Logarithmic functions Hyperbolic Functions sinhx=e'e y=cosh csch-sint天 tanh 1 2 tanhx=sinhx cosh r ohm y=sinh nverse Hyperbolic Functions y=sinhx→sinhy=x sinh 'x In(x+1) y=cosh-1x→coshy=x and y≥0 cosh-lx -In(x+) y=tanh'x←→tanhy=x b)REFERENCE page 4 Exponential and Logarithmic Functions y 1 0 x 1 y=x y=´ y=ln x logb x − y &? by − x ln x − loge x, where ln e − 1 ln x − y &? ey − x Cancellation Equations Laws of Logarithms logbsbx d − x blogb x − x 1. logbsxyd − logb x 1 logb y lnsex d − x eln x − x 2. logbS x y D − logb x 2 logb y 3. logbsxr d − r logb x 4® e® 0 1® 1.5® 10® 2® ” ’ 1 ® 4 ” ’ 1 ® 2 x y 0 y 1 x 1 y=ln x y=log™ x y=log∞ x y=log¡¸ x Exponential functions Logarithmic functions Hyperbolic Functions y x y=sinh x y=cosh x y=tanh x sinh x − ex 2 e2x 2 csch x − 1 sinh x cosh x − ex 1 e2x 2 sech x − 1 cosh x tanh x − sinh x cosh x coth x − cosh x sinh x Inverse Hyperbolic Functions y − sinh21 x &? sinh y − x sinh21 x − lnsx 1 sx 2 1 1d y − cosh21 x &? cosh y − x and y > 0 cosh21 x − lnsx 1 sx 2 2 1d y − tanh21 x &? tanh y − x tanh21 x − 1 2 lnS 1 1 x 1 2 x D lim xl2` ex − 0 lim xl` ex − ` lim xl01 ln x − 2` lim xl` ln x − ` SPECIAL FUNCTIONS Copyright 2021 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it