Mister Exam
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-
How to use it?
- Graphing y =:
- (x^2-x-6)/(x-2)
- 5x^2-3x-1
- -x(x-2)^2
- x/((x-1)*(x-4))
- Limit of the function:
-
sin(x)/(-3+sqrt(9+x))
-
Identical expressions
- sin(x)/(- three +sqrt(nine +x))
- sinus of (x) divide by ( minus 3 plus square root of (9 plus x))
- sinus of (x) divide by ( minus three plus square root of (nine plus x))
- sin(x)/(-3+√(9+x))
- sinx/-3+sqrt9+x
- sin(x) divide by (-3+sqrt(9+x))
-
Similar expressions
- sin(x)/(3+sqrt(9+x))
- sin(x)/(-3-sqrt(9+x))
- sin(x)/(-3+sqrt(9-x))
- sinx/(-3+sqrt(9+x))
Graphing y = sin(x)/(-3+sqrt(9+x))
The solution
You have entered
[src]
sin(x)
f(x) = --------------
_______
-3 + \/ 9 + x
$$f{\left(x \right)} = \frac{\sin{\left(x \right)}}{\sqrt{x + 9} - 3}$$
f = sin(x)/(sqrt(x + 9) - 3)
The graph of the function
The domain of the function
The points at which the function is not precisely defined:
$$x_{1} = 0$$
$$x_{1} = 0$$
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:
$$\frac{\sin{\left(x \right)}}{\sqrt{x + 9} - 3} = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = \pi$$
Numerical solution
$$x_{1} = 65.9734457253857$$
$$x_{2} = 69.1150383789755$$
$$x_{3} = 21.9911485751286$$
$$x_{4} = -40.8407044966673$$
$$x_{5} = -43.9822971502571$$
$$x_{6} = -18.8495559215388$$
$$x_{7} = -3.14159265358979$$
$$x_{8} = -28.2743338823081$$
$$x_{9} = 9.42477796076938$$
$$x_{10} = 97.3893722612836$$
$$x_{11} = -97.3893722612836$$
$$x_{12} = 53.4070751110265$$
$$x_{13} = -69.1150383789755$$
$$x_{14} = 6.28318530717959$$
$$x_{15} = -34.5575191894877$$
$$x_{16} = -50.2654824574367$$
$$x_{17} = 169.646003293849$$
$$x_{18} = 389.557489045134$$
$$x_{19} = -12.5663706143592$$
$$x_{20} = 28.2743338823081$$
$$x_{21} = -47.1238898038469$$
$$x_{22} = -53.4070751110265$$
$$x_{23} = -91.106186954104$$
$$x_{24} = 84.8230016469244$$
$$x_{25} = 59.6902604182061$$
$$x_{26} = 56.5486677646163$$
$$x_{27} = 25.1327412287183$$
$$x_{28} = -62.8318530717959$$
$$x_{29} = 72.2566310325652$$
$$x_{30} = -31.4159265358979$$
$$x_{31} = -37.6991118430775$$
$$x_{32} = 78.5398163397448$$
$$x_{33} = -6.28318530717959$$
$$x_{34} = 37.6991118430775$$
$$x_{35} = -15.707963267949$$
$$x_{36} = 47.1238898038469$$
$$x_{37} = -113.097335529233$$
$$x_{38} = 163.362817986669$$
$$x_{39} = 3.14159265358979$$
$$x_{40} = -56.5486677646163$$
$$x_{41} = 91.106186954104$$
$$x_{42} = -94.2477796076938$$
$$x_{43} = 31.4159265358979$$
$$x_{44} = 43.9822971502571$$
$$x_{45} = 100.530964914873$$
$$x_{46} = 81.6814089933346$$
$$x_{47} = -75.398223686155$$
$$x_{48} = -21.9911485751286$$
$$x_{49} = -87.9645943005142$$
$$x_{50} = 50.2654824574367$$
$$x_{51} = 94.2477796076938$$
$$x_{52} = -84.8230016469244$$
$$x_{53} = 12.5663706143592$$
$$x_{54} = -78.5398163397448$$
$$x_{55} = 18.8495559215388$$
$$x_{56} = 34.5575191894877$$
$$x_{57} = -9.42477796076892$$
$$x_{58} = -65.9734457253857$$
$$x_{59} = -81.6814089933346$$
$$x_{60} = -100.530964914873$$
$$x_{61} = 15.707963267949$$
$$x_{62} = -72.2566310325652$$
$$x_{63} = 87.9645943005142$$
$$x_{64} = -59.6902604182061$$
$$x_{65} = 40.8407044966673$$
$$x_{66} = -25.1327412287183$$
$$x_{67} = 62.8318530717959$$
$$x_{68} = 75.398223686155$$
so we need to solve the equation:
$$\frac{\sin{\left(x \right)}}{\sqrt{x + 9} - 3} = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = \pi$$
Numerical solution
$$x_{1} = 65.9734457253857$$
$$x_{2} = 69.1150383789755$$
$$x_{3} = 21.9911485751286$$
$$x_{4} = -40.8407044966673$$
$$x_{5} = -43.9822971502571$$
$$x_{6} = -18.8495559215388$$
$$x_{7} = -3.14159265358979$$
$$x_{8} = -28.2743338823081$$
$$x_{9} = 9.42477796076938$$
$$x_{10} = 97.3893722612836$$
$$x_{11} = -97.3893722612836$$
$$x_{12} = 53.4070751110265$$
$$x_{13} = -69.1150383789755$$
$$x_{14} = 6.28318530717959$$
$$x_{15} = -34.5575191894877$$
$$x_{16} = -50.2654824574367$$
$$x_{17} = 169.646003293849$$
$$x_{18} = 389.557489045134$$
$$x_{19} = -12.5663706143592$$
$$x_{20} = 28.2743338823081$$
$$x_{21} = -47.1238898038469$$
$$x_{22} = -53.4070751110265$$
$$x_{23} = -91.106186954104$$
$$x_{24} = 84.8230016469244$$
$$x_{25} = 59.6902604182061$$
$$x_{26} = 56.5486677646163$$
$$x_{27} = 25.1327412287183$$
$$x_{28} = -62.8318530717959$$
$$x_{29} = 72.2566310325652$$
$$x_{30} = -31.4159265358979$$
$$x_{31} = -37.6991118430775$$
$$x_{32} = 78.5398163397448$$
$$x_{33} = -6.28318530717959$$
$$x_{34} = 37.6991118430775$$
$$x_{35} = -15.707963267949$$
$$x_{36} = 47.1238898038469$$
$$x_{37} = -113.097335529233$$
$$x_{38} = 163.362817986669$$
$$x_{39} = 3.14159265358979$$
$$x_{40} = -56.5486677646163$$
$$x_{41} = 91.106186954104$$
$$x_{42} = -94.2477796076938$$
$$x_{43} = 31.4159265358979$$
$$x_{44} = 43.9822971502571$$
$$x_{45} = 100.530964914873$$
$$x_{46} = 81.6814089933346$$
$$x_{47} = -75.398223686155$$
$$x_{48} = -21.9911485751286$$
$$x_{49} = -87.9645943005142$$
$$x_{50} = 50.2654824574367$$
$$x_{51} = 94.2477796076938$$
$$x_{52} = -84.8230016469244$$
$$x_{53} = 12.5663706143592$$
$$x_{54} = -78.5398163397448$$
$$x_{55} = 18.8495559215388$$
$$x_{56} = 34.5575191894877$$
$$x_{57} = -9.42477796076892$$
$$x_{58} = -65.9734457253857$$
$$x_{59} = -81.6814089933346$$
$$x_{60} = -100.530964914873$$
$$x_{61} = 15.707963267949$$
$$x_{62} = -72.2566310325652$$
$$x_{63} = 87.9645943005142$$
$$x_{64} = -59.6902604182061$$
$$x_{65} = 40.8407044966673$$
$$x_{66} = -25.1327412287183$$
$$x_{67} = 62.8318530717959$$
$$x_{68} = 75.398223686155$$
Vertical asymptotes
Have:
$$x_{1} = 0$$
$$x_{1} = 0$$
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{\sqrt{x + 9} - 3}\right) = 0$$
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = 0$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{\sqrt{x + 9} - 3}\right) = 0$$
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = 0$$
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{\sqrt{x + 9} - 3}\right) = 0$$
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = 0$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{\sqrt{x + 9} - 3}\right) = 0$$
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = 0$$
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of sin(x)/(-3 + sqrt(9 + x)), divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{x \left(\sqrt{x + 9} - 3\right)}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{x \left(\sqrt{x + 9} - 3\right)}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{x \left(\sqrt{x + 9} - 3\right)}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{x \left(\sqrt{x + 9} - 3\right)}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
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:
$$\frac{\sin{\left(x \right)}}{\sqrt{x + 9} - 3} = - \frac{\sin{\left(x \right)}}{\sqrt{9 - x} - 3}$$
- No
$$\frac{\sin{\left(x \right)}}{\sqrt{x + 9} - 3} = \frac{\sin{\left(x \right)}}{\sqrt{9 - x} - 3}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$\frac{\sin{\left(x \right)}}{\sqrt{x + 9} - 3} = - \frac{\sin{\left(x \right)}}{\sqrt{9 - x} - 3}$$
- No
$$\frac{\sin{\left(x \right)}}{\sqrt{x + 9} - 3} = \frac{\sin{\left(x \right)}}{\sqrt{9 - x} - 3}$$
- No
so, the function
not is
neither even, nor odd