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  • How to use it?

  • Graphing y =:
  • -x^3-3x-2
  • x^3+3x^2+5
  • x^3-3x-20
  • x^3+2x^2+x

  • Identical expressions

  • (one -tan(x))*(log(x)+ two ^x)
  • (1 minus tangent of (x)) multiply by ( logarithm of (x) plus 2 to the power of x)
  • (one minus tangent of (x)) multiply by ( logarithm of (x) plus two to the power of x)
  • (1-tan(x))*(log(x)+2x)
  • 1-tanx*logx+2x
  • (1-tan(x))(log(x)+2^x)
  • (1-tan(x))(log(x)+2x)
  • 1-tanxlogx+2x
  • 1-tanxlogx+2^x

  • Similar expressions

  • (1+tan(x))*(log(x)+2^x)
  • (1-tan(x))*(log(x)-2^x)
Plotting a function graph/ (1-tan(x))*(log(x)+2^x)

Graphing y = (1-tan(x))*(log(x)+2^x)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
                    /          x\
f(x) = (1 - tan(x))*\log(x) + 2 /
f(x)=(1−tan⁡(x))(2x+log⁡(x))f{\left(x \right)} = \left(1 - \tan{\left(x \right)}\right) \left(2^{x} + \log{\left(x \right)}\right) 
f = (1 - tan(x))*(2^x + log(x))
The graph of the function
02468-8-6-4-2-1010-1000010000
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:
(1−tan⁡(x))(2x+log⁡(x))=0\left(1 - \tan{\left(x \right)}\right) \left(2^{x} + \log{\left(x \right)}\right) = 0
Solve this equation
The points of intersection with the axis X:

Numerical solution
x1=16.4933614313464x_{1} = 16.4933614313464
x2=−24.3473430653209x_{2} = -24.3473430653209
x3=41.6261026600648x_{3} = 41.6261026600648
x4=−68.329640215578x_{4} = -68.329640215578
x5=−21.2057504117311x_{5} = -21.2057504117311
x6=32.2013246992954x_{6} = 32.2013246992954
x7=−8.63937979737193x_{7} = -8.63937979737193
x8=−43.1968989868597x_{8} = -43.1968989868597
x9=−5.49778714378214x_{9} = -5.49778714378214
x10=−30.6305283725005x_{10} = -30.6305283725005
x11=−93.4623814442964x_{11} = -93.4623814442964
x12=−77.7544181763474x_{12} = -77.7544181763474
x13=−36.9137136796801x_{13} = -36.9137136796801
x14=−96.6039740978861x_{14} = -96.6039740978861
x15=29.0597320457056x_{15} = 29.0597320457056
x16=−52.621676947629x_{16} = -52.621676947629
x17=−55.7632696012188x_{17} = -55.7632696012188
x18=19.6349540849362x_{18} = 19.6349540849362
x19=−84.037603483527x_{19} = -84.037603483527
x20=25.9181393921158x_{20} = 25.9181393921158
x21=−33.7721210260903x_{21} = -33.7721210260903
x22=−58.9048622548086x_{22} = -58.9048622548086
x23=−46.3384916404494x_{23} = -46.3384916404494
x24=−2.35619449019234x_{24} = -2.35619449019234
x25=−80.8960108299372x_{25} = -80.8960108299372
x26=−87.1791961371168x_{26} = -87.1791961371168
x27=−74.6128255227576x_{27} = -74.6128255227576
x28=−71.4712328691678x_{28} = -71.4712328691678
x29=−14.9225651045515x_{29} = -14.9225651045515
x30=−18.0641577581413x_{30} = -18.0641577581413
x31=−40.0553063332699x_{31} = -40.0553063332699
x32=13.3517687777566x_{32} = 13.3517687777566
x33=−11.7809724509617x_{33} = -11.7809724509617
x34=38.484510006475x_{34} = 38.484510006475
x35=44.7676953136546x_{35} = 44.7676953136546
x36=3.92699081698724x_{36} = 3.92699081698724
x37=−49.4800842940392x_{37} = -49.4800842940392
x38=−90.3207887907066x_{38} = -90.3207887907066
x39=−27.4889357189107x_{39} = -27.4889357189107
x40=10.2101761241668x_{40} = 10.2101761241668
x41=−62.0464549083984x_{41} = -62.0464549083984
x42=−65.1880475619882x_{42} = -65.1880475619882
x43=−99.7455667514759x_{43} = -99.7455667514759
x44=35.3429173528852x_{44} = 35.3429173528852
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to (1 - tan(x))*(log(x) + 2^x).
(1−tan⁡(0))(log⁡(0)+20)\left(1 - \tan{\left(0 \right)}\right) \left(\log{\left(0 \right)} + 2^{0}\right)
The result:
f(0)=∞~f{\left(0 \right)} = \tilde{\infty}
sof doesn't intersect Y
Extrema of the function
In order to find the extrema, we need to solve the equation
ddxf(x)=0\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:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
the first derivative
(1−tan⁡(x))(2xlog⁡(2)+1x)+(2x+log⁡(x))(−tan⁡2(x)−1)=0\left(1 - \tan{\left(x \right)}\right) \left(2^{x} \log{\left(2 \right)} + \frac{1}{x}\right) + \left(2^{x} + \log{\left(x \right)}\right) \left(- \tan^{2}{\left(x \right)} - 1\right) = 0
Solve this equation
The roots of this equation
x1=0.540652930606264x_{1} = 0.540652930606264
The values of the extrema at the points:
(0.5406529306062642, 0.335594586693002)


Intervals of increase and decrease of the function:
Let's find intervals where the function increases and decreases, as well as minima and maxima of the function, for this let's look how the function behaves itself in the extremas and at the slightest deviation from:
The function has no minima
Maxima of the function at points:
x1=0.540652930606264x_{1} = 0.540652930606264
Decreasing at intervals
(−∞,0.540652930606264]\left(-\infty, 0.540652930606264\right]
Increasing at intervals
[0.540652930606264,∞)\left[0.540652930606264, \infty\right)
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
True

Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=lim⁡x→−∞((1−tan⁡(x))(2x+log⁡(x)))y = \lim_{x \to -\infty}\left(\left(1 - \tan{\left(x \right)}\right) \left(2^{x} + \log{\left(x \right)}\right)\right)
True

Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=lim⁡x→∞((1−tan⁡(x))(2x+log⁡(x)))y = \lim_{x \to \infty}\left(\left(1 - \tan{\left(x \right)}\right) \left(2^{x} + \log{\left(x \right)}\right)\right)
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of (1 - tan(x))*(log(x) + 2^x), divided by x at x->+oo and x ->-oo
True

Let's take the limit
so,
inclined asymptote equation on the left:
y=xlim⁡x→−∞((1−tan⁡(x))(2x+log⁡(x))x)y = x \lim_{x \to -\infty}\left(\frac{\left(1 - \tan{\left(x \right)}\right) \left(2^{x} + \log{\left(x \right)}\right)}{x}\right)
True

Let's take the limit
so,
inclined asymptote equation on the right:
y=xlim⁡x→∞((1−tan⁡(x))(2x+log⁡(x))x)y = x \lim_{x \to \infty}\left(\frac{\left(1 - \tan{\left(x \right)}\right) \left(2^{x} + \log{\left(x \right)}\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:
(1−tan⁡(x))(2x+log⁡(x))=(log⁡(−x)+2−x)(tan⁡(x)+1)\left(1 - \tan{\left(x \right)}\right) \left(2^{x} + \log{\left(x \right)}\right) = \left(\log{\left(- x \right)} + 2^{- x}\right) \left(\tan{\left(x \right)} + 1\right)
- No
(1−tan⁡(x))(2x+log⁡(x))=−(log⁡(−x)+2−x)(tan⁡(x)+1)\left(1 - \tan{\left(x \right)}\right) \left(2^{x} + \log{\left(x \right)}\right) = - \left(\log{\left(- x \right)} + 2^{- x}\right) \left(\tan{\left(x \right)} + 1\right)
- No
so, the function
not is
neither even, nor odd
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