Lab_1_Solutions

# Lab_1_Solutions - 1 O O O O O O O O O O O O O O MATH 137...

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Unformatted text preview: 1 O O O O O O O O O O O O O O MATH 137 Maple Lab 1 - Assignment Solutions Mathematical Functions and Bisection Problem 1: Solving Equations 1a) restart : plot 3 \$ cos 3 \$ x , x 2 , x = K 4 ..4, colour = "Red", "Blue" ; K 4 K 3 K 2 K 1 1 2 3 4 K 3 K 2 K 1 1 2 3 1b) fsolve 3 \$ cos 3 \$ x = x 2 , x , K 4 .. K 3 ; K 3.460290751 fsolve 3 \$ cos 3 \$ x = x 2 , x , K 3 .. K 2 ; K 2.778483111 fsolve 3 \$ cos 3 \$ x = x 2 , x , K 2 .. K 1 ; K 1.487298170 fsolve 3 \$ cos 3 \$ x = x 2 , x , K 1 ..0 ; K 0.5544452995 fsolve 3 \$ cos 3 \$ x = x 2 , x , 0 ..1 ; 0.4960111186 2 O O O O O O O O O O O O fsolve 3 \$ cos 3 \$ x = x 2 , x , 1 ..2 ; 1.664497583 fsolve 3 \$ cos 3 \$ x = x 2 , x , 2 ..3 ; 2.476189113 fsolve 3 \$ cos 3 \$ x = x 2 , x , 3 ..4 ; 3.901135962 ANSWER : ANSWER : Thus, the solutions in the interval K 4, 4 are K 3.460290751, K 2.778483111, K 1.487298170, K 0.5544452995, 0.4960111186, 1.664497583, 2.476189113, 3.901135962. Problem 2: The Heaviside Function 2a) restart : f d x / K x K 1 K Heaviside x C 1 \$ K x K 1 C Heaviside x C 1 \$ x K Heaviside x K 1 \$ x C Heaviside x K 1 \$ x K 1 2 ; f := x / K x K 1 K Heaviside x C 1 K x K 1 C Heaviside x C 1 x K Heaviside x K 1 x C Heaviside x K 1 x K 1 2 2b) plot f x , x = K 3 ..3, discont = true ; K 3 K 2 K 1 1 2 3 K 1 1 2 3 4 3 O O O O O O O O Problem 3: Domains and Discontinuities 3a) restart : plot 3.9 \$ x K 2 K x 2 , x = K 1 ..4 ; x K 1 1 2 3 4 K 6 K 5 K 4 K 3 K 2 K 1 1 solve 3.9 \$ x K 2 K x 2 ; 0.6074278418, 3.292572158 fsolve tan 2 \$ x K x , x , 0.6074278418 ..3.292572158 ; 2.137391136 ANSWER : Since \$ is defined only where \$ R 0 , the domain of f x is wherever tan 2 x K x s 0 , and tan 2 x is defined, within the interval 0.6074278418, 3.2925721580....
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## This note was uploaded on 02/21/2010 for the course MATH 137 taught by Professor Speziale during the Spring '08 term at Waterloo.

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Lab_1_Solutions - 1 O O O O O O O O O O O O O O MATH 137...

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