MATH 140 Lecture Notes - Lecture 15: Paper Cup, Airco Dh.2, Quotient Rule

• School: University of Maryland
• Department: Mathematics
• Course: MATH 140
• Professor: Gulick

Document Summary

E4 a: quotient rule: f " ( x)= = y ex e y x ex+ex: plug point in: dy dx. 0e1+e0 = 1 e: equation of the line: y 1=( 1 e)(x, justify why the equation ln x 1 x. Use the newton raphson method and c1 = 1 to find the next approximation c2 of c: determine if there is a zero on [1, e, plug in 1, plug in e: ln 1 1<0 ln e 1 e. >0: since the function is continuous, f(1)<0, and f(e)>0, by the ivt, there must be a zero on the interval [1, e], newton raphson method, formula: c2=c1 f (c1) f " (c1, definitions: a. b. c. c1=1 f ( x)=ln x 1 x. F (1)=ln 1 1= 1 f " ( x)= 1 x. + 1 x2 f "(1)=1+1=2: plug in: c2=1 1.