Let f (x) = x + λ / x, constant λ > 0 If λ = 1, the monotonicity of F (x) on the interval [1,4] is judged and proved 2 if f (x) increases monotonically in the interval [1,4], find the range of λ

Let f (x) = x + λ / x, constant λ > 0 If λ = 1, the monotonicity of F (x) on the interval [1,4] is judged and proved 2 if f (x) increases monotonically in the interval [1,4], find the range of λ

1. The function f (x) is an increasing function in the interval [1,4]
It is proved that let any x 1, x 2 belong to [1,4], and x 10)
F (x1) - f (x2)

Let f (x) = 13x3 − (1 + a) x2 + 4ax + 24a, where the constant a > 1. (1) discuss the monotonicity of F (x); (2) if f (x) > 0 is constant when x ≥ 0, find the value range of A

(1) F ′ (x) = x2-2 (1 + a) x + 4A = (X-2) (x-2a), (2 points) from the known a ＞ 1, ｜ 2A ＞ 2, Let f ′ (x) ＞ 0, the solution is x ＞ 2A or X ＜ 2, Let f ′ (x) ＜ 0, the solution is 2 ＜ x ＜ 2a, (5 points). Therefore, when a ＞ 1, f (x) is an increasing function in the interval (- ∞, 2) and (2a, + ∞)

In a right triangle, the sum of two right angles is greater than the hypotenuse, and the reason is given

The shortest line between two points

What is the set of right angle vertices of right triangle with common hypotenuse? Explain the reason

The vertex of a right triangle is a circle with the diameter of the hypotenuse and the center of the hypotenuse;

If the two right sides of a right triangle are expanded twice at the same time, the hypotenuse will be expanded to the original (); a, 2 times B, 3 times C, 4 times D, 5 times choose a or B

A
Multiple choice questions do not need a process, you can find the number directly

If the two right sides of a right triangle are expanded to three times of the original, how many times of the original is the hypotenuse?

According to the Pythagorean theorem, the bevel should be expanded to 9 times of the original. If you don't understand, please ask. If it helps you, please adopt it. Thank you

If two right angles of a right triangle are enlarged to twice the original, the hypotenuse will be enlarged to the original ()
A. 4 times B. 2 times C. unchanged D. not sure

Let two right angle sides be a and B respectively. According to Pythagorean theorem, hypotenuse = A2 + B2, hypotenuse of expanded right triangle = (2a) 2 + (2b) 2 = 2A2 + B2

At the same time, the two right sides of the right triangle expand to twice the original, and the hypotenuse of the right triangle expands to twice the original______ Times

Let a right triangle be a and B, and its hypotenuse be C, then A2 + B2 = C2; if the hypotenuse is 2 times larger, then the hypotenuse is (2a) 2 + (2b) 2 = 2C according to the Pythagorean theorem. That is to say, if the hypotenuse of a right triangle is 2 times larger, then the hypotenuse is 2 times larger

Calculate the values of the following formulas (accurate to 0.001)
(1) 868;
(2) 426254;
(3) - 8 / 25 cube root;
(4) The cube root of ± 2402

868^(1/3)
ans =
nine point five three nine one
>> 0.426254^(1/3)
ans =
zero point seven five two six
>> (-8/25)^(1/3)
ans =
0.3420 + 0.5924i
2402^(1/3)
ans =
thirteen point three nine two four
>> (-2402)^(1/3)
ans =
6.6962 +11.5981i

If the computer uses 8-bit integer complement to represent data, then () operation will produce overflow. A - 127 + 1 B - 127-1 C 127 + 1 D 127-1 why
I think the expression range of 8-digit integer complement is - 128 ----- 127, which should be 127 + 1 overflow, but the answer is B, so I don't understand. This is a question in the soft test

You only need to know that the 8-bit integer complement indicates that the value range of data (char type variable) is - 128 to 127. Of course, you also need to know what overflow is
127 + 1 =?, is it beyond the scope mentioned above