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-
How to use it?
- Graphing y =:
- x^2+3x+3
- -x^2-2x+1
- (x+1)(x-2)^2
- ((x-1)/(x+1))^3
- Limit of the function:
-
cot(2*x)*tan(7*x)
-
Identical expressions
- cot(two *x)*tan(seven *x)
- cotangent of (2 multiply by x) multiply by tangent of (7 multiply by x)
- cotangent of (two multiply by x) multiply by tangent of (seven multiply by x)
- cot(2x)tan(7x)
- cot2xtan7x
Graphing y = cot(2*x)*tan(7*x)
The solution
You have entered
[src]
f(x) = cot(2*x)*tan(7*x)
$$f{\left(x \right)} = \tan{\left(7 x \right)} \cot{\left(2 x \right)}$$
f = tan(7*x)*cot(2*x)
The graph of the function
The points of intersection with the X-axis coordinate
Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\tan{\left(7 x \right)} \cot{\left(2 x \right)} = 0$$
Solve this equation
The points of intersection with the axis X:
Numerical solution
$$x_{1} = -71.8078320820524$$
$$x_{2} = -75.8470226366679$$
$$x_{3} = -38.484510006475$$
$$x_{4} = -9.87357691128221$$
$$x_{5} = -48.0214877048726$$
$$x_{6} = 4.03919055461545$$
$$x_{7} = -27.8255349317953$$
$$x_{8} = -70.0126362800011$$
$$x_{9} = 36.9137136796801$$
$$x_{10} = 56.0998688141035$$
$$x_{11} = -31.8647254864108$$
$$x_{12} = -4.03919055461545$$
$$x_{13} = -52.060678259488$$
$$x_{14} = -41.738302397693$$
$$x_{15} = -13.9127674658977$$
$$x_{16} = 100.082165964361$$
$$x_{17} = 59.2414614676932$$
$$x_{18} = -92.0037848551297$$
$$x_{19} = 70.0126362800011$$
$$x_{20} = -39.9431065956417$$
$$x_{21} = -79.4374142407705$$
$$x_{22} = 42.1871013482058$$
$$x_{23} = -23.7863443771799$$
$$x_{24} = 8.63937979737193$$
$$x_{25} = 17.9519580205131$$
$$x_{26} = 64.6270488738472$$
$$x_{27} = 74.0518268346165$$
$$x_{28} = 34.1087202389749$$
$$x_{29} = 48.0214877048726$$
$$x_{30} = 46.2262919028212$$
$$x_{31} = 26.030339129744$$
$$x_{32} = -45.7774929523084$$
$$x_{33} = -55.7632696012188$$
$$x_{34} = -74.0518268346165$$
$$x_{35} = 16.1567622184618$$
$$x_{36} = -96.0429754097451$$
$$x_{37} = -5.83438635666676$$
$$x_{38} = 2.24399475256414$$
$$x_{39} = -26.030339129744$$
$$x_{40} = -22.4399475256414$$
$$x_{41} = -77.7544181763474$$
$$x_{42} = 93.4623814442964$$
$$x_{43} = 82.1302079438475$$
$$x_{44} = -53.8558740615393$$
$$x_{45} = -35.9039160410262$$
$$x_{46} = 86.1693984984629$$
$$x_{47} = 61.9342551707702$$
$$x_{48} = 38.484510006475$$
$$x_{49} = 39.9431065956417$$
$$x_{50} = 68.2174404779498$$
$$x_{51} = -97.8381712117964$$
$$x_{52} = 60.1390593687189$$
$$x_{53} = 98.2869701623092$$
$$x_{54} = 64.1782499233343$$
$$x_{55} = -87.5157953500014$$
$$x_{56} = -85.7205995479501$$
$$x_{57} = 92.0037848551297$$
$$x_{58} = 12.1175716638463$$
$$x_{59} = -8.0783811092309$$
$$x_{60} = 78.091017389232$$
$$x_{61} = -89.7597901025655$$
$$x_{62} = -63.7294509728215$$
$$x_{63} = 35.4551170905134$$
$$x_{64} = 20.1959527730772$$
$$x_{65} = 76.2958215871807$$
$$x_{66} = 52.060678259488$$
$$x_{67} = 32.3135244369236$$
$$x_{68} = -57.8950646161548$$
$$x_{69} = -99.7455667514759$$
$$x_{70} = 24.2351433276927$$
$$x_{71} = -62.0464549083984$$
$$x_{72} = -33.7721210260903$$
$$x_{73} = -1.79519580205131$$
$$x_{74} = -19.7471538225644$$
$$x_{75} = 30.0695296843594$$
$$x_{76} = -30.0695296843594$$
$$x_{77} = -58.7926625171804$$
$$x_{78} = -46.2262919028212$$
$$x_{79} = 80.3350121417961$$
$$x_{80} = 90.2085890530783$$
$$x_{81} = 50.7142814079495$$
$$x_{82} = -83.9254037458988$$
$$x_{83} = 38.1479107935903$$
$$x_{84} = -65.07584782436$$
$$x_{85} = 96.0429754097451$$
$$x_{86} = 10.322375861795$$
$$x_{87} = -11.7809724509617$$
$$x_{88} = -17.9519580205131$$
$$x_{89} = -49.8166835069239$$
$$x_{90} = 83.9254037458988$$
$$x_{91} = 21.5423496246157$$
$$x_{92} = 73.1542289335909$$
$$x_{93} = -67.768641527437$$
$$x_{94} = -93.798980657181$$
$$x_{95} = -79.8862131912833$$
$$x_{96} = 54.3046730120521$$
$$x_{97} = 8.0783811092309$$
so we need to solve the equation:
$$\tan{\left(7 x \right)} \cot{\left(2 x \right)} = 0$$
Solve this equation
The points of intersection with the axis X:
Numerical solution
$$x_{1} = -71.8078320820524$$
$$x_{2} = -75.8470226366679$$
$$x_{3} = -38.484510006475$$
$$x_{4} = -9.87357691128221$$
$$x_{5} = -48.0214877048726$$
$$x_{6} = 4.03919055461545$$
$$x_{7} = -27.8255349317953$$
$$x_{8} = -70.0126362800011$$
$$x_{9} = 36.9137136796801$$
$$x_{10} = 56.0998688141035$$
$$x_{11} = -31.8647254864108$$
$$x_{12} = -4.03919055461545$$
$$x_{13} = -52.060678259488$$
$$x_{14} = -41.738302397693$$
$$x_{15} = -13.9127674658977$$
$$x_{16} = 100.082165964361$$
$$x_{17} = 59.2414614676932$$
$$x_{18} = -92.0037848551297$$
$$x_{19} = 70.0126362800011$$
$$x_{20} = -39.9431065956417$$
$$x_{21} = -79.4374142407705$$
$$x_{22} = 42.1871013482058$$
$$x_{23} = -23.7863443771799$$
$$x_{24} = 8.63937979737193$$
$$x_{25} = 17.9519580205131$$
$$x_{26} = 64.6270488738472$$
$$x_{27} = 74.0518268346165$$
$$x_{28} = 34.1087202389749$$
$$x_{29} = 48.0214877048726$$
$$x_{30} = 46.2262919028212$$
$$x_{31} = 26.030339129744$$
$$x_{32} = -45.7774929523084$$
$$x_{33} = -55.7632696012188$$
$$x_{34} = -74.0518268346165$$
$$x_{35} = 16.1567622184618$$
$$x_{36} = -96.0429754097451$$
$$x_{37} = -5.83438635666676$$
$$x_{38} = 2.24399475256414$$
$$x_{39} = -26.030339129744$$
$$x_{40} = -22.4399475256414$$
$$x_{41} = -77.7544181763474$$
$$x_{42} = 93.4623814442964$$
$$x_{43} = 82.1302079438475$$
$$x_{44} = -53.8558740615393$$
$$x_{45} = -35.9039160410262$$
$$x_{46} = 86.1693984984629$$
$$x_{47} = 61.9342551707702$$
$$x_{48} = 38.484510006475$$
$$x_{49} = 39.9431065956417$$
$$x_{50} = 68.2174404779498$$
$$x_{51} = -97.8381712117964$$
$$x_{52} = 60.1390593687189$$
$$x_{53} = 98.2869701623092$$
$$x_{54} = 64.1782499233343$$
$$x_{55} = -87.5157953500014$$
$$x_{56} = -85.7205995479501$$
$$x_{57} = 92.0037848551297$$
$$x_{58} = 12.1175716638463$$
$$x_{59} = -8.0783811092309$$
$$x_{60} = 78.091017389232$$
$$x_{61} = -89.7597901025655$$
$$x_{62} = -63.7294509728215$$
$$x_{63} = 35.4551170905134$$
$$x_{64} = 20.1959527730772$$
$$x_{65} = 76.2958215871807$$
$$x_{66} = 52.060678259488$$
$$x_{67} = 32.3135244369236$$
$$x_{68} = -57.8950646161548$$
$$x_{69} = -99.7455667514759$$
$$x_{70} = 24.2351433276927$$
$$x_{71} = -62.0464549083984$$
$$x_{72} = -33.7721210260903$$
$$x_{73} = -1.79519580205131$$
$$x_{74} = -19.7471538225644$$
$$x_{75} = 30.0695296843594$$
$$x_{76} = -30.0695296843594$$
$$x_{77} = -58.7926625171804$$
$$x_{78} = -46.2262919028212$$
$$x_{79} = 80.3350121417961$$
$$x_{80} = 90.2085890530783$$
$$x_{81} = 50.7142814079495$$
$$x_{82} = -83.9254037458988$$
$$x_{83} = 38.1479107935903$$
$$x_{84} = -65.07584782436$$
$$x_{85} = 96.0429754097451$$
$$x_{86} = 10.322375861795$$
$$x_{87} = -11.7809724509617$$
$$x_{88} = -17.9519580205131$$
$$x_{89} = -49.8166835069239$$
$$x_{90} = 83.9254037458988$$
$$x_{91} = 21.5423496246157$$
$$x_{92} = 73.1542289335909$$
$$x_{93} = -67.768641527437$$
$$x_{94} = -93.798980657181$$
$$x_{95} = -79.8862131912833$$
$$x_{96} = 54.3046730120521$$
$$x_{97} = 8.0783811092309$$
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = \lim_{x \to -\infty}\left(\tan{\left(7 x \right)} \cot{\left(2 x \right)}\right)$$
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = \lim_{x \to \infty}\left(\tan{\left(7 x \right)} \cot{\left(2 x \right)}\right)$$
True
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = \lim_{x \to -\infty}\left(\tan{\left(7 x \right)} \cot{\left(2 x \right)}\right)$$
True
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = \lim_{x \to \infty}\left(\tan{\left(7 x \right)} \cot{\left(2 x \right)}\right)$$
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of cot(2*x)*tan(7*x), divided by x at x->+oo and x ->-oo
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = x \lim_{x \to -\infty}\left(\frac{\tan{\left(7 x \right)} \cot{\left(2 x \right)}}{x}\right)$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = x \lim_{x \to \infty}\left(\frac{\tan{\left(7 x \right)} \cot{\left(2 x \right)}}{x}\right)$$
True
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = x \lim_{x \to -\infty}\left(\frac{\tan{\left(7 x \right)} \cot{\left(2 x \right)}}{x}\right)$$
True
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = x \lim_{x \to \infty}\left(\frac{\tan{\left(7 x \right)} \cot{\left(2 x \right)}}{x}\right)$$
Even and odd functions
Let's check, whether the function even or odd by using relations f = f(-x) и f = -f(-x).
So, check:
$$\tan{\left(7 x \right)} \cot{\left(2 x \right)} = \tan{\left(7 x \right)} \cot{\left(2 x \right)}$$
- Yes
$$\tan{\left(7 x \right)} \cot{\left(2 x \right)} = - \tan{\left(7 x \right)} \cot{\left(2 x \right)}$$
- No
so, the function
is
even
So, check:
$$\tan{\left(7 x \right)} \cot{\left(2 x \right)} = \tan{\left(7 x \right)} \cot{\left(2 x \right)}$$
- Yes
$$\tan{\left(7 x \right)} \cot{\left(2 x \right)} = - \tan{\left(7 x \right)} \cot{\left(2 x \right)}$$
- No
so, the function
is
even