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Judge the number of real number solutions of the equation f (x) = LNX - (2 / x) Judge the number of real number solutions of the equation f (x) = LNX - (2 / x) Judge the number of real number solutions of the equation f (x) = LNX - (2 / x) = 0
Let's say f (x) = 0
lnx=2/x
That is to find the number of intersections of two functions
LNX image in one or four quadrants
2 / X in quadrant 2 / 4
So if there's an intersection in the first quadrant
LNX is an increasing function and 2 / X is a decreasing function
So they have at most one intersection
x=1,lnx=0,2/x=2
X = e, lne = 1, because E > 2, so 2 / E
RELATED INFORMATIONS
- 1. Solve the equation LNX = e + 1-x
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- 3. If f (x) = | LNX | has three intersections with the function y = KX in the interval (0,3), then the value range of K is
- 4. If the intersection of the line y = KX + 2K + 1 and the line y = − 12x + 2 is in the first quadrant, then the value range of K is () A. −12＜k＜12B. −16＜k＜12C. k＞12D. k＞−12
- 5. Given that the two intersections of two curves y = KX + 1 and x ^ 2-y-8 = 0 are symmetric about the Y axis, then the coordinates of the two intersections are
- 6. It is known that hyperbola C1 and hyperbola C2: y ^ 2 / 4-x ^ 2 / 9 = 1 have the same asymptote And through the point m (9 / 2, - 1), the standard equation of hyperbola C1 is obtained
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- 8. As shown in the figure, the left and right fixed points of ellipse C1: x ^ 2 / 4 + y ^ 2 / 3 = 1 are a, B and P respectively, which are a point on the right branch (above the X axis) of hyperbola C2: x ^ 2 / 4-y ^ 2 / 3 = 1 Connecting AP is called C1 to C, connecting Pb and extending the intersection C1 to D, and the areas of △ ACD and △ PCD are equal. Calculate the slope of the straight line PD and the inclination angle of the straight line CD
- 9. It is known that the image of a function y = KX + B passes through a point (- 2,5), and the intersection of the line y = - 3 / 2x + 3 and the Y axis is symmetric about the X axis Find the analytic expression of this function
- 10. Given y = 2x + if the line y = KX + B is symmetric to the given line about the Y axis, find the values of K and B
- 11. The derivative of X + LNX
- 12. How to use the definition to find the derivative of LNX,
- 13. It is known that the right quasilinear of two hyperbolas is x = 4, the right focus is f (10.0), and the eccentricity is e = 2?
- 14. Given that the eccentricity of hyperbola is 2, the focus is (4,0), (- 4,0), then what is the hyperbolic equation? Help me if you know
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- 16. Let the eccentricity of hyperbola be √ 5 / 2 and have a common focus with the square of ellipse x2 / 9 + the square of Y2 / 4 = 1
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- 18. Given that the right focus of the hyperbola x2a2-y25 = 1 is (3,0), then the eccentricity of the hyperbola is equal to () A. 31414B. 324C. 32D. 43
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