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How to prove that the series Σ f (n) {Q} / T (n) {P} has the same convergence as the series Σ 1 / N ^ (P-Q)? Where Q and P are the largest power of N in the function
F (n) {Q} / T (n) {P} is the quotient of two polynomials. The numerator is Q times and the denominator is p times. Now, the series Σ 1 / N ^ (P-Q) is used for comparison, so: Lim [f (n) {Q} / T (n) {P}] / [1 / N ^ (P-Q)] = Lim [f (n) {Q + P} / T (n) {P + Q}] = constant (i.e. the quotient of the coefficient of the highest power of the two polynomials), so the series Σ f (n) {Q} / T (n) {P
Continuous functions on open intervals must be bounded. A. error B. correct
A. Error, the limit at both ends of the open interval must exist before it is bounded
The function y = x / (x ^ 2 + 1) is bounded in (- ∞, + ∞). How to prove it
|y| = |x|/x^2+1
Y = 0 when x = 0
When x ≠ 0 | y | = 1 / (| x | + 1 / | x |)
How to prove that y = (x ^ 6 + x ^ 4 + x ^ 2) / (1 + x ^ 6) is a bounded function
When | x | ≤ 1, x ^ 6 ≤ 1, x ^ 4 ≤ 1, x ^ 2 ≤ 1, 0 ≤ y ≤ 3 / (1 + x ^ 6) ≤ 3
When | x | > 1, x ^ 4
It is proved that the function y = (x + 2) / (x ^ 2 + 1) is a bounded function Is there a way to avoid derivation.
1、 When x = - 2, y = 0. 2. When x ≠ - 2, let x + 2 = a, then: y = A / [(A-2) ^ 2 + 1] = A / (a ^ 2-4a + 5) = 1 / (a + 5 / A-4). 1. When a > 0, there is: Y > 0. Obviously, there are: a + 5 / a ≥ 2 √ 5, a + 5 / A-4 ≥ 2 √ 5-4, 11 / (a + 5 / A-4) ≤ 1 /
The derivative in the function, I only know a problem, and then find the derivative, find the slope, and the differential, I only know to find the derivative, and then add DX to the result. It feels too shallow. The book says that the derivative is to find the instantaneous quantity of independent variables and tangent problems, and I don't understand the differential at all,
Every function has a change trend, and the derivative is to find the change trend. Taking speed as an example, the derivative of speed to time is acceleration, that is, the speed of speed change
RELATED INFORMATIONS
- 1. Proof of differential mean value theorem in Advanced Mathematics Let a > b > 0, prove that A-B / a < ln a / b < A-B / b
- 2. It is known that the image of the quadratic function y = (m-1) x2 + M2-1 with respect to x passes through (0,3) and the parabolic opening is downward (1) Find the value of M; (2) Find the distance between the two intersections of this parabola and the X axis Now,
- 3. Let the function f (x) = f (1 / x) * lgx + 1, then the value of F (10) is
- 4. Given that the function f (x) is an increasing function on R, a, B ∈ R, it is proved that if f (a) + F (b) > F (- a) + F (- b), then a + b > 0
- 5. It is known that f (x) has f (AB) = f (a) + F (b) for any real number a and B 1) Find the values of F (1) and f (0) 2) If f (2) = P, f (3) = q (both P and Q are constants), find the value of F (36) 3) Verify that f (1 / x) = - f (x)
- 6. It is proved that the limit LIM (x + y) / (X-Y) does not exist when x approaches 0 and Y approaches 0
- 7. Use fzero in MATLAB to solve the root of equation x ^ 2. * exp (- x ^ 2) = 0.2 in interval [- 2,2]?
- 8. The image of function f (x) in interval [a, b] is a continuous curve. Why is it continuous
- 9. Known function y = (1) 4)x−(1 2) The definition field of X + 1 is [- 3, 2], (1) Find the monotone interval of the function; (2) Find the value range of the function
- 10. The equation of motion of an object is s = T ^ 3 + 2T ^ 2-1. When t = 2,
- 11. F (x) is monotonically bounded in the positive and negative infinite interval, and xn is a sequence. If xn is monotonic, then f (x) converges? If f (x) = 1 / X and xn = 1 / N, this conclusion is not tenable
- 12. Given the function f (x) = (x ^ 2-x-1 / a) e ^ ax (a > 0) (1) when a = 1, find the monotone interval (2) of function f (x) if the inequality f (x) + 5 / a ≥ 0 vs x ∈ Known function f (x) = (x ^ 2-x-1 / a) e ^ ax (a > 0) (1) When a = 1, find the monotone interval of function f (x) (2) If the inequality f (x) + 5 / a ≥ 0 holds for X ∈ R, find the value range of A
- 13. The monotonically decreasing interval of the function f (x) = |logax| (a > 0 and a ≠ 1) is __
- 14. ★ if the definition field of function f (x + 1) = x ^ 2-2x + 1 is (- 2,0), the decreasing interval of F (x) is ()
- 15. Find the [(2x + 1) / (x-1) power of the definition field and value field F (x) = 3 of the function Because 3 / X-1 belongs to R, all values are not equal to 0 What do you mean? Analyze it in detail and the one behind it
- 16. If a series of functions have the same analytical formula, the same value range, but different definition fields, these functions are called "homologous functions", and the "homologous functions" with the analytical formula of y = x2 and the value range of {1,4} share () A. 7 B. 8 C. 9 D. 10
- 17. Is the total differential of a binary function the partial derivative?
- 18. Let the function z = x / y. find the total differential dz| (2,1)
- 19. Several limit problems lin (x^3-3x+2)/(x-1)^2= x->+∞ lin [1/x(sinx)+xsin(1/x)]= x->+∞ Please give the solution process, the more detailed the better, and teach how to find the limit such as 0 / 0 and ∞ / ∞
- 20. Questions about the idea of using the definition of definite integral to solve the limit of sequence sum formula or definite integral problem, Which of the following ideas is right when using the definition of definite integral to solve the limit of sum of sequence or definite integral problem? 1. First write down the idea that "it has been verified that this limit exists or meets the existence condition of definite integral"; 2. This kind of problem has recognized limit or definite integral. There is no need to write anything. You can directly use the definition of definite integral to solve it. This idea is also clear (recognized!); 3. Isn't it circular logic to write that assumes existence or not and assumes existence by default? That is, when seeking a value, first assume its existence, and then use the existence to deduce the value, so as to obtain that the assumption is correct, which is similar to proving yourself?