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Given f (x + 1) = x2-3x + 2, find the value of F (radical 2)
f(x+1)=x^2-3x+2
f(x)=(x-1)^2-3(x-1)+2=x^2-5x+6
f(√2)=(√2)^2-5√2+6=8-5√2
seek
The maximum value of F (x) = (x2 + 1) - x under the root sign
In [0, positive infinity]
Let: 0 ＜ x1 ＜ x2 X1 ^ 2 ＜ x2 ^ 2 √ (x1 ^ 2 + 1) ＜√ (x2 ^ 2 + 1) √ (x1 ^ 2 + 1) + X ＜√ (x2 ^ 2 + 1) + X ∵ f (x) = √ (x ^ 2 + 1) - x = 1 / (√ (x ^ 2 + 1) + x) ∵ f (x2) - f (x1) ＜ 0f (x) = root sign (x ^ 2 + 1) - X be a decreasing function in [0, + infinity], that is, when x = 0, there is a maximum value of:
It is verified that the function f (x) = root x satisfies Lagrange mean value theorem in [4,9],
f(x)=√x,f'(x)=1/(2√x)=[f(4)-f(9)]/(4-9)=1/5.
four
Solving equation x / (1-24%) = 4 4x = 8 / 25
X/(1-24%)=4
X/0.76=4
X=4*0.76
X=3.04
4X = 8 / 25
X=8/25÷4
X=2/25
Cut a 10 cm long and 8 cm wide rectangular cardboard into the largest circle. The utilization rate of this paper is ()%
10x8=80cm²
3.14x4x4=50.24cm²
50.24÷80x100%=62.8%
Physics: speed equals the speed of a moving object in ()
Distance per unit time
If 2x ^ NY ^ 4 and m ^ 2x ^ M-N are all the six degree monomials of X and y, and the coefficients are equal, find the value of M and n
The number of C is 6
So n + 4 = 6, n = 2
And | M-N | = 6
m-2=±6
M = - 4 or 8
Coefficient 2 = 1 / 2m & # 178;
m²=4
m=±2
M has no solution
So there is no solution
A circular paper is cut into two sectors along the radius, and the ratio of the central angle of the circle is 3:4. Then they are rolled into two sides of the cone, and the volume ratio of the two cones is obtained
3:4
Solve and check the following simple equation problems
1.4+x=6
2.x-5=8
1
x=2
2+2=6
two
x=13
13-5=8
Let f (x) for any real number x1, X2, have f (x1 + x2) = f (x1) * f (x2), and f '(0) = 1, prove that f' (x) = f (x)
F (x) for any real number x1, X2, f (x1 + x2) = f (x1) * f (x2), take x2 = 0, f (x1) = f (x1) f (0) so f (0) = 1, so f '(x) = LIM (H - > 0) [f (x + H) - f (x)] / h = LIM (H - > 0) [f (x)) f (H) - f (x)] / h = f (x) LIM (H - > 0) [f (H) - 1] / h = f (x) LIM (H - > 0) [f (H) - f (0)] / h = f (x) * f' (0) =
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