It is proved that the function f (x) = x + 1 / X is monotonically increasing on (0,1] It's decreasing

It is proved that the function f (x) = x + 1 / X is monotonically increasing on (0,1] It's decreasing

Proof: let 0

Find the definition domain, period and monotone increasing interval of the function y = TaNx + | TaNx | and draw a sketch
Thank you~

Discussion in different cases: when x ∈ (- X / 2 + K y,], we discuss it once
A discussion on X ∈ (k, Y / 2 + K, y)
The definition and field x ≠ K п + / 2
Period
Monotone increasing interval: (k, Y / 2 + K, y)
Draw your own pictures!

The function y = f (x) defined on [- 1,1] is a decreasing function and an odd function. If f (a ^ 2-a-1) + F (4a-5) is greater than 0, the range of a is obtained

f(a^2-a-1)+f(4a-5)>0=>f(a^2-a-1)>-f(4a-5)
∵ f (x) is an odd function
∴-f(4a-5)=f(5-4a)
∴f(a^2-a-1)>f(5-4a)
And f (x) is a decreasing function
∴ -1

Are 3 × 2 & # 178; and 2 × 3 & # 178; similar or not

3 × 2 & # 178; and 2 × 3 & # 178; are not of the same kind

If f (x) = x * 2-2ax + 2 (x > = 1) has an inverse function, then the value range of a is____
As the title!

∵ f (x) has inverse function
The monotonicity of F (x) on X ≥ 1
The symmetry axis X = a of quadratic function should be on the left side of 1
∴a≤1

Write f (x) = x | x | - 2x + 1 as a piecewise function, and then draw the function image

x> When f = 0, f (x) = x ^ 2-2x + 1;
x

The function of one variable exists between limit, continuous, differentiable, integrable
What is the relationship between the existence limit, continuity, differentiability, and integrability of functions of one variable? What is the relationship between functions of many variables?

One yuan:
Derivable must be continuous, continuous must have limit, (unidirectional)
Differentiable and derivable mutual inference
multivariate:
First order partial derivative continuously derivable differentiable, (unidirectional)
Differentiable derivation (1) existence of partial derivative (unidirectional)
(2) Function continuous (unidirectional)
The existence of double limit of function
//
If and only if f (x0) = LIM (x → x0) f (x) is continuous at x0, that is to say, the value of function exists at this point and is equal to the limit value of this point
If the derivative of a function exists at a certain point, it is said that it is differentiable at this point, otherwise it is said that it is not differentiable. The necessary and sufficient condition of differentiability is that the function must be continuous at this point, and the left derivative is equal to the right reciprocal. (our teacher once introduced a function derived by Weierstrass and Weierstrass, which is continuous but not differentiable everywhere. If you are interested, you can check it.)
Differentiability is equivalent to differentiability in functions of one variable. In functions of many variables, the existence of partial derivatives of variables at this point is a necessary and sufficient condition. In addition, in the generalized surface represented by this function, there is no "hole" in the field of this point, and there can be a finite number of breakpoints
There are only sufficient conditions for function integrability: ① function is continuous in the interval; ② function is discontinuous in the interval, but there are only a limited number of discontinuities of the first kind (jumping discontinuities, removable discontinuities). The above conditions are actually Riemannian integrable conditions, which can be relaxed, so they are only sufficient conditions
Differentiable must be continuous, continuous is not necessarily differentiable, that is to say, derivation is a sufficient condition for continuity, and continuity is a necessary condition for differentiability
Differentiability is equivalent to differentiability in univariate function, differentiability must be differentiable in multivariate function, differentiability is not necessarily differentiable, differentiability is the sufficient condition of differentiability, differentiability is the necessary condition of differentiability
So the strength is differentiable, differentiable and continuous
There is no necessary relationship between Integrability and differentiability

The n-order symmetric matrix problem a and B are two n-order symmetric matrices. It is proved that ab + Ba is symmetric matrix and ab-ba is antisymmetric matrix
A and B are two symmetric matrices of order n. It is proved that ab + Ba are symmetric matrices
Ab-ba is an antisymmetric matrix

A and B are two symmetric matrices of order n, a ^ t = A and B ^ t = B
(AB+BA)^T=(AB)^T+(BA)^T=B^TA^T+A^TB^T=AB+BA
So AB + Ba is a symmetric matrix
same
(AB－BA)^T=(AB)^T-(BA)^T=B^TA^T-A^TB^T=BA-AB
So ab-ba is antisymmetric matrix

For nouns ending with a consonant letter and y, change y to I, and then add es. for nouns ending with a vowel letter and y, add s directly, followed by a vowel sign or a vowel letter?

When the ending of consonant letter + y is changed into I, and then es and proper nouns ending with y are added, or the ending of vowel letter + y is changed into plural, directly add s to change plural, baby --- babies consonant letter + y is changed into proper nouns ending with y, or vowel letter + y is changed into proper nouns ending with y

1 / 2lg32 / 49-4 / 3lg √ 8 + LG √ 245 how to calculate, let alone calculator

1/2lg32/49-4/3lg√8+lg√245
=1/2lg32/49+1/2lg245-1/3lg64
=1/2lg160-lg4
=1/2lg160-1/2lg16
=1/2lg10
=1/2
You should know some basic knowledge: algb = LG (b ^ a)
lga+lgb=lg(a*b)
lga-lgb=lg(a/b)
Understand these questions