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Project: week4
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#6 #(a) Q(t)=100*e^(-10.0019*t) plot(Q(t),(t,0,0.1),color='green')+point((0.00,100.00))+point((0.02,81.87))+point((0.04,67.03))+point((0.06,54.88))+point((0.08,44.93))+point((0.10,36.76))
Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python3.8/site-packages/smc_sagews/sage_server.py", line 1211, in execute locals) File "", line 1, in <module> File "sage/misc/session.pyx", line 216, in sage.misc.session.show_identifiers (build/cythonized/sage/misc/session.c:2160) from sage.doctest.forker import DocTestTask File "/ext/sage/sage-8.9_1804/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 57, in <module> from .sources import DictAsObject File "/ext/sage/sage-8.9_1804/local/lib/python2.7/site-packages/sage/doctest/sources.py", line 33, in <module> from .parsing import SageDocTestParser File "/ext/sage/sage-8.9_1804/local/lib/python2.7/site-packages/sage/doctest/parsing.py", line 34, in <module> from Cython.Build.Dependencies import strip_string_literals as cython_strip_string_literals File "/ext/sage/sage-8.9_1804/local/lib/python2.7/site-packages/Cython/Build/__init__.py", line 2, in <module> from .Distutils import build_ext File "/ext/sage/sage-8.9_1804/local/lib/python2.7/site-packages/Cython/Build/Distutils.py", line 1, in <module> from Cython.Distutils.build_ext import build_ext File "/ext/sage/sage-8.9_1804/local/lib/python2.7/site-packages/Cython/Distutils/__init__.py", line 1, in <module> from Cython.Distutils.build_ext import build_ext File "/ext/sage/sage-8.9_1804/local/lib/python2.7/site-packages/Cython/Distutils/build_ext.py", line 11, in <module> from distutils.command.build_ext import build_ext as _build_ext File "/ext/sage/sage-8.9_1804/local/lib/python2.7/distutils/command/build_ext.py", line 16, in <module> from distutils.sysconfig import customize_compiler, get_python_version File "/ext/sage/sage-8.9_1804/local/lib/python2.7/distutils/sysconfig.py", line 283, in <module> _findvar2_rx = re.compile(r"\${([A-Za-z][A-Za-z0-9_]*)}") File "/ext/sage/sage-8.9_1804/local/lib/python2.7/re.py", line 194, in compile return _compile(pattern, flags) File "/ext/sage/sage-8.9_1804/local/lib/python2.7/re.py", line 249, in _compile p = sre_compile.compile(pattern, flags) File "/ext/sage/sage-8.9_1804/local/lib/python2.7/sre_compile.py", line 576, in compile code = _code(p, flags) File "/ext/sage/sage-8.9_1804/local/lib/python2.7/sre_compile.py", line 561, in _code _compile(code, p.data, flags) File "/ext/sage/sage-8.9_1804/local/lib/python2.7/sre_compile.py", line 151, in _compile _compile(code, av[1], flags) File "/ext/sage/sage-8.9_1804/local/lib/python2.7/sre_compile.py", line 132, in _compile _compile(code, av[2], flags) File "/ext/sage/sage-8.9_1804/local/lib/python2.7/sre_compile.py", line 107, in _compile _compile_charset(av, flags, code, fixup, fixes) File "/ext/sage/sage-8.9_1804/local/lib/python2.7/sre_compile.py", line 242, in _compile_charset code.extend(av) File "src/cysignals/signals.pyx", line 320, in cysignals.signals.python_check_interrupt KeyboardInterrupt
#(b) dQ(t)=diff(Q(t),t) dQ(t) dQ(0.04)
-1000.19000000000*e^(-10.0019000000000*t) -670.396454777669
#7 var('t,a,k') assume(k>0) p(t)=1/(1+a*e^(-k*t)) #(a) limit(p(t),t=+oo)
(t, a, k) 1
#(b) dp(t)=diff(p(t),t) dp(t)
a*k*e^(-k*t)/(a*e^(-k*t) + 1)^2
#(c) p(t)=1/(1+10*e^(-0.5*t)) plot(p(t),t,0,10) find_root(p(t)==0.8,6,8)
7.3777589082278725
#9 var('r,t') x=r(t-sin(t)) y=r(1-cos(t)) parametric_plot((x,y),(t,-2*pi,2*pi))
(r, t)
#(a) a(t)=diff(x,t) b(t)=diff(y,t) a(t),b(t) print(b(pi/3)/a(pi/3)) #y=sqrt(3)*x-(sqrt(3)*pi/3-2)*r
(-cos(t) + 1, sin(t)) sqrt(3)
#(b) horizontal:pi+2n*pi vertical:2n*pi find_root(b(t)/a(t)==0,-2*pi,2*pi)
-3.141592653589793
lim(b(t)/a(t),t=0) lim(b(t)/a(t),t=2*pi)
Infinity Infinity
#(c) x=(t-sin(t)) y=(1-cos(t)) parametric_plot((x,y),(t,-pi,pi))+plot(sqrt(3)*t-(sqrt(3)*pi/3-2),(t,-pi,pi))