2511.sagews

limit((sin(3*x)/x),x=0)

3

p=plot((sin(3*x)/x),x,-10,10)                          
pt=point((0,3),rgbcolor='yellow',pointsize=30,faceted=true)
g=p+pt                                                     
g.show(xmin=-10,xmax=10,ymin=-10,ymax=10)

limit((1-cos(5*x)/x),x=0)

Infinity

Limit((sin(1-x)/sqrt(x)-1)),x=0)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_5.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("TGltaXQoKHNpbigxLXgpL3NxcnQoeCktMSkpLHg9MCk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpfi3T1M/___code___.py", line 3 Limit((sin(_sage_const_1 -x)/sqrt(x)-_sage_const_1 )),x=_sage_const_0 ) ^ SyntaxError: invalid syntax

Limit((sin(1-x)/(sqrt(x)-1)),x=0)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_6.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("TGltaXQoKHNpbigxLXgpLyhzcXJ0KHgpLTEpKSx4PTAp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpHFPiNp/___code___.py", line 3, in <module> exec compile(u'Limit((sin(_sage_const_1 -x)/(sqrt(x)-_sage_const_1 )),x=_sage_const_0 )' + '\n', '', 'single') File "", line 1, in <module> NameError: name 'Limit' is not defined

limit((sin(1-x)/(sqrt(x)-1)),x=0)

-sin(1)

p=plot((sin(1-x)/(sqrt(x)-1)),x,-10,10)                          
pt=point((0,-sin(1)),rgbcolor='yellow',pointsize=30,faceted=true)
g=p+pt                                                     
g.show(xmin=-10,xmax=10,ymin=-10,ymax=10)

verbose 0 (3495: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 100 points. verbose 0 (3495: plot.py, generate_plot_points) Last error message: ''

limit((tan(x)-sin(x))/(x^3),x=0)

1/2

p=plot((tan(x)-sin(x))/(x^3),x,-10,10)                          
pt=point((0,1/2),rgbcolor='yellow',pointsize=30,faceted=true)
g=p+pt                                                     
g.show(xmin=-10,xmax=10,ymin=-10,ymax=10)