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It is proved that f (x) = X-1 / X is an increasing function in the interval (0, positive infinity) It's x minus 1 / X. it's a detailed process. Thank you~~~
On the interval (0, positive infinity), let X1 > x2 > 0
f(x1)-f(x2)=x1-1/x1-x2+1/x2=（X1X2+1)(X1-X2)/(X1+X2)
Because x1-x2 > 0, x1x2 > 0
Therefore, f (x1) - f (x2) > 0
That is, f (x1) > F (x2)
Therefore, it is a monotone increasing function in the interval (0, positive infinity)
It is proved that the function f (x) = (x + 1) / (x + 2) is an increasing function in the interval (- 2, positive infinity)
f(x)=(x+1)/(x+2)=1-1/(x+2)
It is proved by the definition of function monotonicity that f (x) = a ^ x + A ^ (- x) is an increasing function on (0, positive infinity) (where a > 0 and a is not equal to 1)
For any X1 > x2 > 0f (x1) - f (x2) = a ^ X1 + A ^ (- x1) - A ^ x2-a ^ (- x2) = (a ^ x1-a ^ x2) + [a ^ (- x1) - A ^ (- x2)] = (a ^ x1-a ^ x2) + (1 / A ^ x1-1 / A ^ x2) = (a ^ x1-a ^ x2) + (a ^ x2-a ^ x1) / A ^ x1 × a ^ x2 = (a ^ x1-a ^ x2) (1-1 / A ^ x1 × a ^ x2) if 00, f (x1) > F (x2), f (x) in (0, + ∞
It is proved that f (x) = x ^ 2 + 1 / X is a monotone increasing function on (1, positive infinity)
Such as the title
f(x)=x^2+（1/x）
Make a difference
Let P > 1, Q > 1, P > Q
f(p) = p^2 + 1/p
f(q) = q^2 + 1/q
F (P) is greater than f (q) because
f(p)-f(q) = ( p^2 + 1/p) - ( q^2 + 1/q)
= (p^2 - q^2) + (1/p - 1/q)
=(p+q)(p-q) + (q-p)/pq
= (p-q)(p+q-1/pq)
p> Q, so P-Q > 0
p> 1, Q > 1, so 1 / PQ 1 + 1 - 1 > 0
So f (P) - f (q) > 0
f(p) >f(q)
So f (x) = x ^ 2 + 1 / X is a monotone increasing function on (1, positive infinity)
Using a △ B equal to a / B to solve the calculation problem skillfully: (6.4 × 480 × 33.3) △ 3.2 × 120 × 66.6)
（6.4×480×33.3）÷（3.2×120×66.6）=6.4/3.2×480/120×33.3/66.6=2×4×1/2=4
What is 2 minus 1516 divided by 57 divided by 34
2-1516/57/34 = 1.2177502579979
(2-1516)/57/34 = -0.781217750258
Judging right and wrong, applying the law of operation can make the calculation simple
Wrong, choosing the right method is the key, otherwise it may become more and more complicated
Simple method of 0.74 * 0.25 + 0.75
0.74*0.25+0.75
=0.74*0.25+0.25*3
=0.47*(0.25+3)
=0.47*3.25
=1.5275
It is known that the solution of the system of equations {2x-3y = 2, MX + 2Y = 5 about X, y is the solution of the equation x-2y = 3, and the value of M is obtained. Someone first solved the system of equations {2x-3y = 2, x-2y = 3, and then substituted its solution into MX + 2Y = 5 to get M. do you think his method is right? If it is right, explain the reason, and find the value of m according to his method; if not, give your solution
That's right
It is equivalent to using three equations to solve three unknowns. First get two, then get the last one
① What is the quotient of 6 minus the product of 1 / 4 and 2 / 5 and dividing it by 1 / 4? 2. 50% of 76 is more than 7 times of a number. 3. Find this number
A square land with a circumference of 60 cm is equal to a triangle land with a height of 20 meters. What is the bottom of the triangle land?
23.6
five
ten
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