The limit of F (x) is a, a > 0. It is proved that f (x) is equal to a under the triple root sign Can be added!

Let: LIM (x - > x0) f (x) = a > 0, prove: LIM (x - > x0) √ f (x) = √ a [to prove certain, take the limit when X - > x0, other limit processes are the same; √ a represents the cube root of a & sup3; √ a] prove: ① for any ε > 0, ∵ LIM (x - > x0) f (x) = a > 0

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1. X divided by (1-radical x + 1) (x is greater than or equal to negative 1. X is not equal to 0)
2. How much is the limit when x is close to zero
3. Given the function f (x) = ax & # 178; - (2a & # 178; - 1) x-2a (a ∈ R), let the solution set of the inequality f (x) > 0 be a, and also know that B = {x | 1 ＜ x ＜ 3}, a ∩ B ≠ & # 216;, and find the value range of A
4. The known function f (x) = - 2A & # 178; X & # 178; + ax + 1 If f (x) = - 2A & # 178; X & # 178; + ax + 1 ≤ 0 is constant in the interval (1, + ∞), find the value range of real number a
5. Given the function f (x) = & # 188; X & # 8308; = & # 8531; ax & # 179; - A & # 178; X & # 178; + A & # 8308; (a > 0), find the monotone interval of the function
6. Given the function f (x) = x cube minus 4x & # 178; 1) find the monotone interval of function f (x) (2) find the function f (x) in the closed interval 0 The known function f (x) = x cube minus 4x & # 178; 1) Finding monotone interval of function f (x) (2) Finding the maximum and minimum of function f (x) in the closed interval 0 4
7. If the function f (x) = ax & # 178; + BX + 3A + B defined on [a-1,2a] is even, then a + B =?
8. The function f (x) is even and is a decreasing function on (- ∞ 0). Try to compare the size of F (- 7 / 8) and f (2a & # 178; - A + 1)
9. Given that even function f (x) (x ≠ 0) is monotone on interval (0, + ∞), what is the sum of all x satisfying f (X & # 178; - 2x-1) = f (x + 1)?
10. If f (x) = (K-3) x & # 178; + (K-2) x + 3 is an even function, then the increasing interval of the function is________
11. F (x) = [(x ^ 2 under the third radical) - (x under the second radical)] divide by X (x > = 0) to find the limit of F (x) at x = 0 F (x) = [(x ^ 2 under the third radical) - (x under the second radical)] divide by X (x > = 0) to find the limit of F (x) at x = 0
12. How to understand the instantaneous change rate of point derivative? When the increment of the independent variable approaches the limit of 0, that is, the instantaneous rate of change of the point derivative of the point, the problem is why the increment of the independent variable is still meaningful when it is all 0, and why there is still a rate of change when there is no change at the point?
13. Take a point (1,2) and a nearby point (1 + △ x, 2 + △ y) on the image of curve y = x2 + 1, then △ y △ x is______ ．
14. Is derivative the instantaneous rate of change Just learning derivative, it's a bit abstract for me, I can't help but be grateful!
15. The problem of derivative in second grade mathematics Find the tangent equation of the curve y = SiNx at point a (6 / 6 π, 2 parts only 1)? 2. Find the tangent equation of the square of the parabola y = x parallel to the line 2x-y = 0? 3. Find the tangent equation of the point (0,0) and the square of the curve y = x? 4. Find the tangent equation of the point (1, - 1) on the curve y = XD 3 power - 2x? To write the process, thank you
16. It is known that f (x) is an odd function defined on R. when x ≥ 0, f (x) = x2-2x, then the expression of F (x) on R is () A. y=x（x-2）B. y=x（|x|-1）C. y=|x|（x-2）D. y=x（|x|-2）
17. It is known that the quadratic function f (x) = ax + BX (a, B are familiar, and a ≠ 0) satisfies the following conditions: F (- x + 5) = f (x-3), and the equation f (x) = x has equal roots (1) The expression of finding f (x) (2) whether there is a teacher's uncle m, n (m) or not
18. It is known that the quadratic function f (x) = ax ^ 2 + BX (AB ∈ R, a ≠ 0) satisfies f (- x + 5) = f (x-3) and the equation f (x) = x has equal roots; It is known that the quadratic function f (x) = ax ^ 2 + BX (AB ∈ R, a ≠ 0) satisfies f (- x + 5) = f (x-3) and the equation f (x) = x has equal roots. (1) find the analytic expression of F (x); (2) whether there are real numbers m, n (m < n), so that the domain of definition and value of F (x) are [M, n] and [3M, 3N]? If there are, find the value of M, N; if not, explain the reason
19. It is known that the quadratic function f (x) = ax ^ 2 + BX satisfies f (2) = 0 and the equation f (x) = x has equal roots
20. If the quadratic function f (x) = AX2 + BX + C, if f (0) = 0 and f (x + 1) = f (x) + X + 1, then f (x)=