Mister Exam
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- Curve in 3D space defined parametrically
- Area between lines
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How to use it?
- Graphing y =:
- (sqrt(cos(x))*cos(75x)+sqrt(abs(x))-0,7)*(4-x*x)^0.2,sqrt(9-x^2),-sqrt(9-x^2),-x
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xe^(-x)
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xlnx
- y=2log2(x-1)
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Identical expressions
- (sqrt(cos(x))*cos(seven 5x)+sqrt(abs(x))- zero ,7)*(four -x*x)^ zero . two ,sqrt(nine -x^ two),-sqrt(nine -x^ two),-x
- ( square root of ( co sinus of e of (x)) multiply by co sinus of e of (75x) plus square root of (abs(x)) minus 0,7) multiply by (4 minus x multiply by x) to the power of 0.2, square root of (9 minus x squared ), minus square root of (9 minus x squared ), minus x
- ( square root of ( co sinus of e of (x)) multiply by co sinus of e of (seven 5x) plus square root of (abs(x)) minus zero ,7) multiply by (four minus x multiply by x) to the power of zero . two , square root of (nine minus x to the power of two), minus square root of (nine minus x to the power of two), minus x
- (√(cos(x))*cos(75x)+√(abs(x))-0,7)*(4-x*x)^0.2,√(9-x^2),-√(9-x^2),-x
- (sqrt(cos(x))*cos(75x)+sqrt(abs(x))-0,7)*(4-x*x)0.2,sqrt(9-x2),-sqrt(9-x2),-x
- sqrtcosx*cos75x+sqrtabsx-0,7*4-x*x0.2,sqrt9-x2,-sqrt9-x2,-x
- (sqrt(cos(x))*cos(75x)+sqrt(abs(x))-0,7)*(4-x*x)^0.2,sqrt(9-x²),-sqrt(9-x²),-x
- (sqrt(cos(x))*cos(75x)+sqrt(abs(x))-0,7)*(4-x*x) to the power of 0.2,sqrt(9-x to the power of 2),-sqrt(9-x to the power of 2),-x
- (sqrt(cos(x))cos(75x)+sqrt(abs(x))-0,7)(4-xx)^0.2,sqrt(9-x^2),-sqrt(9-x^2),-x
- (sqrt(cos(x))cos(75x)+sqrt(abs(x))-0,7)(4-xx)0.2,sqrt(9-x2),-sqrt(9-x2),-x
- sqrtcosxcos75x+sqrtabsx-0,74-xx0.2,sqrt9-x2,-sqrt9-x2,-x
- sqrtcosxcos75x+sqrtabsx-0,74-xx^0.2,sqrt9-x^2,-sqrt9-x^2,-x
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Similar expressions
- (sqrt(cos(x))*cos(75x)-sqrt(abs(x))-0,7)*(4-x*x)^0.2,sqrt(9-x^2),-sqrt(9-x^2),-x
- (sqrt(cos(x))*cos(75x)+sqrt(abs(x))+0,7)*(4-x*x)^0.2,sqrt(9-x^2),-sqrt(9-x^2),-x
- (sqrt(cos(x))*cos(75x)+sqrt(abs(x))-0,7)*(4-x*x)^0.2,sqrt(9-x^2),-sqrt(9+x^2),-x
- (sqrt(cos(x))*cos(75x)+sqrt(abs(x))-0,7)*(4-x*x)^0.2,sqrt(9-x^2),-sqrt(9-x^2),+x
- (sqrt(cos(x))*cos(75x)+sqrt(abs(x))-0,7)*(4+x*x)^0.2,sqrt(9-x^2),-sqrt(9-x^2),-x
- (sqrt(cos(x))*cos(75x)+sqrt(abs(x))-0,7)*(4-x*x)^0.2,sqrt(9-x^2),+sqrt(9-x^2),-x
- (sqrt(cos(x))*cos(75x)+sqrt(abs(x))-0,7)*(4-x*x)^0.2,sqrt(9+x^2),-sqrt(9-x^2),-x
- (sqrt(cosx)*cos(75x)+sqrt(abs(x))-0,7)*(4-x*x)^0.2,sqrt(9-x^2),-sqrt(9-x^2),-x
Plotting a function graph/
(sqrt(cos(x))*cos(75x)+sqrt(abs(x))-0,7)*(4-x*x)^0.2,sqrt(9-x^2),-sqrt(9-x^2),-x
Graphing y = (sqrt(cos(x))*cos(75x)+sqrt(abs(x))-0,7)*(4-x*x)^0.2,sqrt(9-x^2),-sqrt(9-x^2),-x
The solution
You have entered
[src]
________ ________
/ ________ _____ 7 \ 5 _________ / 2 / 2
f(x) = (|\/ cos(x) *cos(75*x) + \/ |x| - --|*\/ 4 - x*x , \/ 9 - x , -\/ 9 - x , -x)
\ 10/
$$f{\left(x \right)} = \left( \sqrt[5]{- x x + 4} \left(\left(\sqrt{\cos{\left(x \right)}} \cos{\left(75 x \right)} + \sqrt{\left|{x}\right|}\right) - \frac{7}{10}\right), \ \sqrt{9 - x^{2}}, \ - \sqrt{9 - x^{2}}, \ - x\right)$$
f = ((-x*x + 4)^(1/5)*(sqrt(cos(x))*cos(75*x) + sqrt(|x|) - 7/10, sqrt(9 - x^2), -sqrt(9 - x^2), -x))
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:
$$\left( \sqrt[5]{- x x + 4} \left(\left(\sqrt{\cos{\left(x \right)}} \cos{\left(75 x \right)} + \sqrt{\left|{x}\right|}\right) - \frac{7}{10}\right), \ \sqrt{9 - x^{2}}, \ - \sqrt{9 - x^{2}}, \ - x\right) = 0$$
Solve this equation
Solution is not found,
it's possible that the graph doesn't intersect the axis X
so we need to solve the equation:
$$\left( \sqrt[5]{- x x + 4} \left(\left(\sqrt{\cos{\left(x \right)}} \cos{\left(75 x \right)} + \sqrt{\left|{x}\right|}\right) - \frac{7}{10}\right), \ \sqrt{9 - x^{2}}, \ - \sqrt{9 - x^{2}}, \ - x\right) = 0$$
Solve this equation
Solution is not found,
it's possible that the graph doesn't intersect the axis X
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
$$\frac{d}{d x} \left( \sqrt[5]{- x x + 4} \left(\left(\sqrt{\cos{\left(x \right)}} \cos{\left(75 x \right)} + \sqrt{\left|{x}\right|}\right) - \frac{7}{10}\right), \ \sqrt{9 - x^{2}}, \ - \sqrt{9 - x^{2}}, \ - x\right) = 0$$
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
$$\frac{d}{d x} \left( \sqrt[5]{- x x + 4} \left(\left(\sqrt{\cos{\left(x \right)}} \cos{\left(75 x \right)} + \sqrt{\left|{x}\right|}\right) - \frac{7}{10}\right), \ \sqrt{9 - x^{2}}, \ - \sqrt{9 - x^{2}}, \ - x\right) = 0$$
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
$$\frac{d^{2}}{d x^{2}} \left( \sqrt[5]{- x x + 4} \left(\left(\sqrt{\cos{\left(x \right)}} \cos{\left(75 x \right)} + \sqrt{\left|{x}\right|}\right) - \frac{7}{10}\right), \ \sqrt{9 - x^{2}}, \ - \sqrt{9 - x^{2}}, \ - x\right) = 0$$
Solve this equation
Solutions are not found,
maybe, the function has no inflections
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(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
$$\frac{d^{2}}{d x^{2}} \left( \sqrt[5]{- x x + 4} \left(\left(\sqrt{\cos{\left(x \right)}} \cos{\left(75 x \right)} + \sqrt{\left|{x}\right|}\right) - \frac{7}{10}\right), \ \sqrt{9 - x^{2}}, \ - \sqrt{9 - x^{2}}, \ - x\right) = 0$$
Solve this equation
Solutions are not found,
maybe, the function has no inflections
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
Limit on the left could not be calculated
$$\lim_{x \to -\infty} \left( \sqrt[5]{- x x + 4} \left(\left(\sqrt{\cos{\left(x \right)}} \cos{\left(75 x \right)} + \sqrt{\left|{x}\right|}\right) - \frac{7}{10}\right), \ \sqrt{9 - x^{2}}, \ - \sqrt{9 - x^{2}}, \ - x\right)$$
Limit on the right could not be calculated
$$\lim_{x \to \infty} \left( \sqrt[5]{- x x + 4} \left(\left(\sqrt{\cos{\left(x \right)}} \cos{\left(75 x \right)} + \sqrt{\left|{x}\right|}\right) - \frac{7}{10}\right), \ \sqrt{9 - x^{2}}, \ - \sqrt{9 - x^{2}}, \ - x\right)$$
Limit on the left could not be calculated
$$\lim_{x \to -\infty} \left( \sqrt[5]{- x x + 4} \left(\left(\sqrt{\cos{\left(x \right)}} \cos{\left(75 x \right)} + \sqrt{\left|{x}\right|}\right) - \frac{7}{10}\right), \ \sqrt{9 - x^{2}}, \ - \sqrt{9 - x^{2}}, \ - x\right)$$
Limit on the right could not be calculated
$$\lim_{x \to \infty} \left( \sqrt[5]{- x x + 4} \left(\left(\sqrt{\cos{\left(x \right)}} \cos{\left(75 x \right)} + \sqrt{\left|{x}\right|}\right) - \frac{7}{10}\right), \ \sqrt{9 - x^{2}}, \ - \sqrt{9 - x^{2}}, \ - x\right)$$