Mister Exam
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-
How to use it?
- Graphing y =:
- x^3+3x^2-2
-
x^1/3
- 2x^3+3x^2+1
- y=tan(x+5)
-
Identical expressions
- y=tan(x+ five)
- y equally tangent of (x plus 5)
- y equally tangent of (x plus five)
- y=tanx+5
-
Similar expressions
- tan(x)+(5/2)
- y=tan(x-5)
- 2*atan((x+5)/(2-x))
Graphing y = y=tan(x+5)
The solution
You have entered
[src]
f(x) = tan(x + 5)
$$f{\left(x \right)} = \tan{\left(x + 5 \right)}$$
f = tan(x + 5)
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:
$$\tan{\left(x + 5 \right)} = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = -5$$
Numerical solution
$$x_{1} = 10.707963267949$$
$$x_{2} = -77.2566310325652$$
$$x_{3} = -30.1327412287183$$
$$x_{4} = -55.2654824574367$$
$$x_{5} = 4.42477796076938$$
$$x_{6} = 48.4070751110265$$
$$x_{7} = -74.1150383789755$$
$$x_{8} = 73.5398163397448$$
$$x_{9} = 26.4159265358979$$
$$x_{10} = 7.56637061435917$$
$$x_{11} = -83.5398163397448$$
$$x_{12} = 16.9911485751286$$
$$x_{13} = 29.5575191894877$$
$$x_{14} = -64.6902604182061$$
$$x_{15} = -99.2477796076938$$
$$x_{16} = -33.2743338823081$$
$$x_{17} = -86.6814089933346$$
$$x_{18} = 57.8318530717959$$
$$x_{19} = 92.3893722612836$$
$$x_{20} = -80.398223686155$$
$$x_{21} = 98.6725575684632$$
$$x_{22} = 86.106186954104$$
$$x_{23} = 76.6814089933346$$
$$x_{24} = 35.8407044966673$$
$$x_{25} = -5$$
$$x_{26} = -61.5486677646163$$
$$x_{27} = -11.2831853071796$$
$$x_{28} = 23.2743338823081$$
$$x_{29} = 32.6991118430775$$
$$x_{30} = 1.28318530717959$$
$$x_{31} = 13.8495559215388$$
$$x_{32} = 38.9822971502571$$
$$x_{33} = -45.8407044966673$$
$$x_{34} = 20.1327412287183$$
$$x_{35} = -42.6991118430775$$
$$x_{36} = 42.1238898038469$$
$$x_{37} = 89.2477796076938$$
$$x_{38} = -20.707963267949$$
$$x_{39} = -70.9734457253857$$
$$x_{40} = -52.1238898038469$$
$$x_{41} = -1.85840734641021$$
$$x_{42} = 95.5309649148734$$
$$x_{43} = -89.8230016469244$$
$$x_{44} = -17.5663706143592$$
$$x_{45} = -48.9822971502571$$
$$x_{46} = -39.5575191894877$$
$$x_{47} = 64.1150383789755$$
$$x_{48} = 45.2654824574367$$
$$x_{49} = -67.8318530717959$$
$$x_{50} = 82.9645943005142$$
$$x_{51} = 79.8230016469244$$
$$x_{52} = 60.9734457253857$$
$$x_{53} = 67.2566310325652$$
$$x_{54} = -8.14159265358979$$
$$x_{55} = -26.9911485751286$$
$$x_{56} = -36.4159265358979$$
$$x_{57} = 54.6902604182061$$
$$x_{58} = -23.8495559215388$$
$$x_{59} = 70.398223686155$$
$$x_{60} = 51.5486677646163$$
$$x_{61} = -14.4247779607694$$
$$x_{62} = -58.4070751110265$$
$$x_{63} = -92.9645943005142$$
$$x_{64} = -96.106186954104$$
so we need to solve the equation:
$$\tan{\left(x + 5 \right)} = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = -5$$
Numerical solution
$$x_{1} = 10.707963267949$$
$$x_{2} = -77.2566310325652$$
$$x_{3} = -30.1327412287183$$
$$x_{4} = -55.2654824574367$$
$$x_{5} = 4.42477796076938$$
$$x_{6} = 48.4070751110265$$
$$x_{7} = -74.1150383789755$$
$$x_{8} = 73.5398163397448$$
$$x_{9} = 26.4159265358979$$
$$x_{10} = 7.56637061435917$$
$$x_{11} = -83.5398163397448$$
$$x_{12} = 16.9911485751286$$
$$x_{13} = 29.5575191894877$$
$$x_{14} = -64.6902604182061$$
$$x_{15} = -99.2477796076938$$
$$x_{16} = -33.2743338823081$$
$$x_{17} = -86.6814089933346$$
$$x_{18} = 57.8318530717959$$
$$x_{19} = 92.3893722612836$$
$$x_{20} = -80.398223686155$$
$$x_{21} = 98.6725575684632$$
$$x_{22} = 86.106186954104$$
$$x_{23} = 76.6814089933346$$
$$x_{24} = 35.8407044966673$$
$$x_{25} = -5$$
$$x_{26} = -61.5486677646163$$
$$x_{27} = -11.2831853071796$$
$$x_{28} = 23.2743338823081$$
$$x_{29} = 32.6991118430775$$
$$x_{30} = 1.28318530717959$$
$$x_{31} = 13.8495559215388$$
$$x_{32} = 38.9822971502571$$
$$x_{33} = -45.8407044966673$$
$$x_{34} = 20.1327412287183$$
$$x_{35} = -42.6991118430775$$
$$x_{36} = 42.1238898038469$$
$$x_{37} = 89.2477796076938$$
$$x_{38} = -20.707963267949$$
$$x_{39} = -70.9734457253857$$
$$x_{40} = -52.1238898038469$$
$$x_{41} = -1.85840734641021$$
$$x_{42} = 95.5309649148734$$
$$x_{43} = -89.8230016469244$$
$$x_{44} = -17.5663706143592$$
$$x_{45} = -48.9822971502571$$
$$x_{46} = -39.5575191894877$$
$$x_{47} = 64.1150383789755$$
$$x_{48} = 45.2654824574367$$
$$x_{49} = -67.8318530717959$$
$$x_{50} = 82.9645943005142$$
$$x_{51} = 79.8230016469244$$
$$x_{52} = 60.9734457253857$$
$$x_{53} = 67.2566310325652$$
$$x_{54} = -8.14159265358979$$
$$x_{55} = -26.9911485751286$$
$$x_{56} = -36.4159265358979$$
$$x_{57} = 54.6902604182061$$
$$x_{58} = -23.8495559215388$$
$$x_{59} = 70.398223686155$$
$$x_{60} = 51.5486677646163$$
$$x_{61} = -14.4247779607694$$
$$x_{62} = -58.4070751110265$$
$$x_{63} = -92.9645943005142$$
$$x_{64} = -96.106186954104$$
Extrema of the function
In order to find the extrema, we need to solve the equation
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d x} f{\left(x \right)} = $$
the first derivative
$$\tan^{2}{\left(x + 5 \right)} + 1 = 0$$
Solve this equation
Solutions are not found,
function may have no extrema
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d x} f{\left(x \right)} = $$
the first derivative
$$\tan^{2}{\left(x + 5 \right)} + 1 = 0$$
Solve this equation
Solutions are not found,
function may have no extrema
Inflection points
Let's find the inflection points, we'll need to solve the equation for this
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
the second derivative
$$2 \left(\tan^{2}{\left(x + 5 \right)} + 1\right) \tan{\left(x + 5 \right)} = 0$$
Solve this equation
The roots of this equation
$$x_{1} = -5$$
Сonvexity and concavity intervals:
Let’s find the intervals where the function is convex or concave, for this look at the behaviour of the function at the inflection points:
Concave at the intervals
$$\left[-5, \infty\right)$$
Convex at the intervals
$$\left(-\infty, -5\right]$$
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
the second derivative
$$2 \left(\tan^{2}{\left(x + 5 \right)} + 1\right) \tan{\left(x + 5 \right)} = 0$$
Solve this equation
The roots of this equation
$$x_{1} = -5$$
Сonvexity and concavity intervals:
Let’s find the intervals where the function is convex or concave, for this look at the behaviour of the function at the inflection points:
Concave at the intervals
$$\left[-5, \infty\right)$$
Convex at the intervals
$$\left(-\infty, -5\right]$$
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
$$\lim_{x \to -\infty} \tan{\left(x + 5 \right)} = \left\langle -\infty, \infty\right\rangle$$
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = \left\langle -\infty, \infty\right\rangle$$
$$\lim_{x \to \infty} \tan{\left(x + 5 \right)} = \left\langle -\infty, \infty\right\rangle$$
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = \left\langle -\infty, \infty\right\rangle$$
$$\lim_{x \to -\infty} \tan{\left(x + 5 \right)} = \left\langle -\infty, \infty\right\rangle$$
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = \left\langle -\infty, \infty\right\rangle$$
$$\lim_{x \to \infty} \tan{\left(x + 5 \right)} = \left\langle -\infty, \infty\right\rangle$$
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = \left\langle -\infty, \infty\right\rangle$$
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of tan(x + 5), divided by x at x->+oo and x ->-oo
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = x \lim_{x \to -\infty}\left(\frac{\tan{\left(x + 5 \right)}}{x}\right)$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = x \lim_{x \to \infty}\left(\frac{\tan{\left(x + 5 \right)}}{x}\right)$$
True
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = x \lim_{x \to -\infty}\left(\frac{\tan{\left(x + 5 \right)}}{x}\right)$$
True
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = x \lim_{x \to \infty}\left(\frac{\tan{\left(x + 5 \right)}}{x}\right)$$
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:
$$\tan{\left(x + 5 \right)} = - \tan{\left(x - 5 \right)}$$
- No
$$\tan{\left(x + 5 \right)} = \tan{\left(x - 5 \right)}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$\tan{\left(x + 5 \right)} = - \tan{\left(x - 5 \right)}$$
- No
$$\tan{\left(x + 5 \right)} = \tan{\left(x - 5 \right)}$$
- No
so, the function
not is
neither even, nor odd