MATH 1505 Lecture Notes - Lecture 5: Implicit Function, Asymptote

• School: York University
• Department: Mathematics and Statistics
• Course: MATH 1505
• Professor: Natasha May

Document Summary

Sinx"=cosx cosx"=-sinx tanx=sec2x cotx=-csc2x secx=secx tanx cscx=-cscx cotx lim x 0 sinx x. =1 e h 1 h lim h 0. =0 e x"=e x a x"=ln ( a) ax a g( x)"=ln (a) a g(x) g( x )" e g (x)"=g ( x)" e g (x) f 1 ( x )= 1 f " [ f 1 ( x )] arctanx "=tan 1 (x ) "= 1. 1+ x 2 arcsinx "=sin 1( x ) "= 1. 1 x 2 ln x "= 1 x loga x "= 1 (lna) x loga g ( x)"= System of equaions (fog)"(x) = f"[g(x)]g"(x) now we can easily see that there is a vertical asymptote at x = 3. Because it crossed out it isn"t a vertical asymptote but there will be a hole in the graph. It won"t affect it too much its just protocol to keep the original domain intact at all times.