Mister Exam
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-
How to use it?
- Graphing y =:
-
x/x^2+1
- x/(x^2-1)
- xe^(1/x)
- xcosx
-
Identical expressions
- (four ^x- three)(log[ four , seventeen - two ^x])tan[x/ two ]/(log[ sixteen ,x]- zero . five)
- (4 to the power of x minus 3)( logarithm of [4,17 minus 2 to the power of x]) tangent of [x divide by 2] divide by ( logarithm of [16,x] minus 0.5)
- (four to the power of x minus three)( logarithm of [ four , seventeen minus two to the power of x]) tangent of [x divide by two ] divide by ( logarithm of [ sixteen ,x] minus zero . five)
- (4x-3)(log[4,17-2x])tan[x/2]/(log[16,x]-0.5)
- 4x-3log[4,17-2x]tan[x/2]/log[16,x]-0.5
- 4^x-3log[4,17-2^x]tan[x/2]/log[16,x]-0.5
- (4^x-3)(log[4,17-2^x])tan[x divide by 2] divide by (log[16,x]-0.5)
-
Similar expressions
- (4^x+3)(log[4,17-2^x])tan[x/2]/(log[16,x]-0.5)
- (4^x-3)(log[4,17+2^x])tan[x/2]/(log[16,x]-0.5)
- (4^x-3)(log[4,17-2^x])tan[x/2]/(log[16,x]+0.5)
Graphing y = (4^x-3)(log[4,17-2^x])tan[x/2]/(log[16,x]-0.5)
The solution
You have entered
[src]
/ x \ /417 x\ /x\
\4 - 3/*log|--- - 2 |*tan|-|
\100 / \2/
f(x) = -----------------------------
log(16) 1
------- - -
log(x) 2
$$f{\left(x \right)} = \frac{\left(4^{x} - 3\right) \log{\left(\frac{417}{100} - 2^{x} \right)} \tan{\left(\frac{x}{2} \right)}}{- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(x \right)}}}$$
f = (((4^x - 3)*log(417/100 - 2^x))*tan(x/2))/(-1/2 + log(16)/log(x))
The graph of the function
The domain of the function
The points at which the function is not precisely defined:
$$x_{1} = 1$$
$$x_{2} = 256$$
$$x_{1} = 1$$
$$x_{2} = 256$$
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:
$$\frac{\left(4^{x} - 3\right) \log{\left(\frac{417}{100} - 2^{x} \right)} \tan{\left(\frac{x}{2} \right)}}{- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(x \right)}}} = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = \frac{\log{\left(3 \right)}}{2 \log{\left(2 \right)}}$$
$$x_{2} = \log{\left(\left(\frac{317}{100}\right)^{\frac{1}{\log{\left(2 \right)}}} \right)}$$
Numerical solution
$$x_{1} = -69.1150383789755$$
$$x_{2} = -12.5663706143592$$
$$x_{3} = -25.1327412287183$$
$$x_{4} = -50.2654824574367$$
$$x_{5} = -43.9822971502571$$
$$x_{6} = 0$$
$$x_{7} = -37.6991118430775$$
$$x_{8} = -31.4159265358979$$
$$x_{9} = -56.5486677646163$$
$$x_{10} = -94.2477796076938$$
$$x_{11} = 1.66448284036468$$
$$x_{12} = 12.5663706143592$$
$$x_{13} = -62.8318530717959$$
$$x_{14} = -87.9645943005142$$
$$x_{15} = -81.6814089933346$$
$$x_{16} = 6.28318530717959$$
$$x_{17} = -75.398223686155$$
$$x_{18} = 18.8495559215388$$
$$x_{19} = -100.530964914873$$
$$x_{20} = -6.28318530717959$$
$$x_{21} = 1$$
$$x_{22} = -18.8495559215388$$
$$x_{23} = 0.792481250360578$$
so we need to solve the equation:
$$\frac{\left(4^{x} - 3\right) \log{\left(\frac{417}{100} - 2^{x} \right)} \tan{\left(\frac{x}{2} \right)}}{- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(x \right)}}} = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = \frac{\log{\left(3 \right)}}{2 \log{\left(2 \right)}}$$
$$x_{2} = \log{\left(\left(\frac{317}{100}\right)^{\frac{1}{\log{\left(2 \right)}}} \right)}$$
Numerical solution
$$x_{1} = -69.1150383789755$$
$$x_{2} = -12.5663706143592$$
$$x_{3} = -25.1327412287183$$
$$x_{4} = -50.2654824574367$$
$$x_{5} = -43.9822971502571$$
$$x_{6} = 0$$
$$x_{7} = -37.6991118430775$$
$$x_{8} = -31.4159265358979$$
$$x_{9} = -56.5486677646163$$
$$x_{10} = -94.2477796076938$$
$$x_{11} = 1.66448284036468$$
$$x_{12} = 12.5663706143592$$
$$x_{13} = -62.8318530717959$$
$$x_{14} = -87.9645943005142$$
$$x_{15} = -81.6814089933346$$
$$x_{16} = 6.28318530717959$$
$$x_{17} = -75.398223686155$$
$$x_{18} = 18.8495559215388$$
$$x_{19} = -100.530964914873$$
$$x_{20} = -6.28318530717959$$
$$x_{21} = 1$$
$$x_{22} = -18.8495559215388$$
$$x_{23} = 0.792481250360578$$
Vertical asymptotes
Have:
$$x_{1} = 1$$
$$x_{2} = 256$$
$$x_{1} = 1$$
$$x_{2} = 256$$
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:
$$y = \lim_{x \to -\infty}\left(\frac{\left(4^{x} - 3\right) \log{\left(\frac{417}{100} - 2^{x} \right)} \tan{\left(\frac{x}{2} \right)}}{- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(x \right)}}}\right)$$
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = \lim_{x \to \infty}\left(\frac{\left(4^{x} - 3\right) \log{\left(\frac{417}{100} - 2^{x} \right)} \tan{\left(\frac{x}{2} \right)}}{- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(x \right)}}}\right)$$
True
Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = \lim_{x \to -\infty}\left(\frac{\left(4^{x} - 3\right) \log{\left(\frac{417}{100} - 2^{x} \right)} \tan{\left(\frac{x}{2} \right)}}{- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(x \right)}}}\right)$$
True
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = \lim_{x \to \infty}\left(\frac{\left(4^{x} - 3\right) \log{\left(\frac{417}{100} - 2^{x} \right)} \tan{\left(\frac{x}{2} \right)}}{- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(x \right)}}}\right)$$
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of (((4^x - 3)*log(417/100 - 2^x))*tan(x/2))/(log(16)/log(x) - 1/2), divided by x at x->+oo and x ->-oo
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = x \lim_{x \to -\infty}\left(\frac{\left(4^{x} - 3\right) \log{\left(\frac{417}{100} - 2^{x} \right)} \tan{\left(\frac{x}{2} \right)}}{x \left(- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(x \right)}}\right)}\right)$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = x \lim_{x \to \infty}\left(\frac{\left(4^{x} - 3\right) \log{\left(\frac{417}{100} - 2^{x} \right)} \tan{\left(\frac{x}{2} \right)}}{x \left(- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(x \right)}}\right)}\right)$$
True
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = x \lim_{x \to -\infty}\left(\frac{\left(4^{x} - 3\right) \log{\left(\frac{417}{100} - 2^{x} \right)} \tan{\left(\frac{x}{2} \right)}}{x \left(- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(x \right)}}\right)}\right)$$
True
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = x \lim_{x \to \infty}\left(\frac{\left(4^{x} - 3\right) \log{\left(\frac{417}{100} - 2^{x} \right)} \tan{\left(\frac{x}{2} \right)}}{x \left(- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(x \right)}}\right)}\right)$$
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:
$$\frac{\left(4^{x} - 3\right) \log{\left(\frac{417}{100} - 2^{x} \right)} \tan{\left(\frac{x}{2} \right)}}{- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(x \right)}}} = - \frac{\left(-3 + 4^{- x}\right) \log{\left(\frac{417}{100} - 2^{- x} \right)} \tan{\left(\frac{x}{2} \right)}}{- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(- x \right)}}}$$
- No
$$\frac{\left(4^{x} - 3\right) \log{\left(\frac{417}{100} - 2^{x} \right)} \tan{\left(\frac{x}{2} \right)}}{- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(x \right)}}} = \frac{\left(-3 + 4^{- x}\right) \log{\left(\frac{417}{100} - 2^{- x} \right)} \tan{\left(\frac{x}{2} \right)}}{- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(- x \right)}}}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$\frac{\left(4^{x} - 3\right) \log{\left(\frac{417}{100} - 2^{x} \right)} \tan{\left(\frac{x}{2} \right)}}{- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(x \right)}}} = - \frac{\left(-3 + 4^{- x}\right) \log{\left(\frac{417}{100} - 2^{- x} \right)} \tan{\left(\frac{x}{2} \right)}}{- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(- x \right)}}}$$
- No
$$\frac{\left(4^{x} - 3\right) \log{\left(\frac{417}{100} - 2^{x} \right)} \tan{\left(\frac{x}{2} \right)}}{- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(x \right)}}} = \frac{\left(-3 + 4^{- x}\right) \log{\left(\frac{417}{100} - 2^{- x} \right)} \tan{\left(\frac{x}{2} \right)}}{- \frac{1}{2} + \frac{\log{\left(16 \right)}}{\log{\left(- x \right)}}}$$
- No
so, the function
not is
neither even, nor odd