Lab9temp 151 22C 2 Jupyter Notebook 11 17 22 1 57 PM MATH 151 Lab 9 Put team members names and section number here In 2 from sympy import from sympy plotting import plot plot parametric Question 1 In 3 print lny xln 1 26 x print f x ln 1 26 x print g x 1 x lny xln 1 26 x f x ln 1 26 x g x 1 x In 4 x symbols x f ln 1 26 x g 1 x limf limit f x oo limg limit g x oo print limit as f oo is limf print limit as g oo is limg limit as f oo is 0 limit as g oo is 0 1a 1b 1c http localhost 8888 notebooks Downloads Lab9temp 151 22C 2 ipynb MATH 151 Lab 8 Page 1 of 5 Lab9temp 151 22C 2 Jupyter Notebook 11 17 22 1 57 PM In 5 df diff f x dg diff g x lim df dg print lim print As x oo lny 26 1 26 oo 26 1 print Therefore according to L hospital s rule the limit is equal to exp 26 26 1 26 x As x oo lny 26 1 26 oo 26 1 Therefore according to L hospital s rule the limit is equal to ex p 26 In 6 y 1 26 x x lm limit y x oo print According to python the limit is lm so it matches the answer in part c According to python the limit is exp 26 so it matches the answer in part c Question 2 1d 2a 2b In 7 width 42 8 height 50 20 diagonal width 2 height 2 diagonal diagonal 4 radius sqrt diagonal print Radius of billboard has to be radius inches Radius of billboard has to be 43 0116263352131 inches http localhost 8888 notebooks Downloads Lab9temp 151 22C 2 ipynb MATH 151 Lab 8 Page 2 of 5 Lab9temp 151 22C 2 Jupyter Notebook 11 17 22 1 57 PM In 8 w symbols w h symbols h radius 55 w sqrt 110 2 h 2 8 area w h area 110 2 h 2 1 2 h dA diff area h height solve dA h width sqrt 110 2 height 1 2 8 height height 1 20 print f Dimensions are height x width inches Dimensions are 57 7817459305202 x 69 7817459305202 inches Question 3 3a In 15 R2 2R1 volume 590 R symbols R h 1770 pi 7 R 2 SA pi 3 R sqrt R 2 h 2 pi 5 R 2 OP diff SA R plot SA R 0 5 ylim 300 800 print Optimization function is OP factor IC 10 00 3b Optimization function is 2 147 pi 2 R 6 35 pi R 5 sqrt 49 p i 2 R 2 3132900 R 4 4699350 7 R 4 sqrt 49 pi 2 R 2 3132900 R 4 http localhost 8888 notebooks Downloads Lab9temp 151 22C 2 ipynb MATH 151 Lab 8 Page 3 of 5 Lab9temp 151 22C 2 Jupyter Notebook 11 17 22 1 57 PM In 19 cv nsolve OP 2 8 print R1 cv print R2 cv 2 print h h subs R cv evalf R1 2 73235307040265 R2 5 46470614080531 h 10 7808181056803 Question 4 x symbols x C symbols C f 5 x 1 2 f1 integrate f x C Ceqn f1 subs x 0 3 Cval solve Ceqn C f1 f1 Cval 0 f2 integrate f1 x C Ceqn f2 subs x 0 9 Cval solve Ceqn C print f f2 Cval 0 4a In 21 4b In 31 f C x C 8 5 log x 1 9 C1 C2 symbols C1 C2 f1 integrate f x C1 f2 integrate f1 x C2 eq1 f2 subs x 1 10 eq2 f2 subs x 4 10 c1 5 log 2 10 C2 eq2 eq2 subs C1 c1 c2 solve eq2 C2 c2 c2 0 C c1 subs C2 c2 function f2 subs C1 C function function subs C2 c2 print f function f x 5 log 2 3 5 log 5 3 5 log x 1 5 log 5 3 20 log 2 3 10 http localhost 8888 notebooks Downloads Lab9temp 151 22C 2 ipynb MATH 151 Lab 8 Page 4 of 5 Lab9temp 151 22C 2 Jupyter Notebook 11 17 22 1 57 PM http localhost 8888 notebooks Downloads Lab9temp 151 22C 2 ipynb MATH 151 Lab 8 Page 5 of 5
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