F (x) = x ^ 2 - ax + ln (x + 1), a belongs to R F extremum when a = 2 If the function f (x) always has f prime (x) greater than x in the interval (0,1), find the value range of real number a

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• 1. It is known that f (x) = ln (AX + 1) + x ^ 3-x ^ 2-ax If f (x) is an increasing function on [1, positive infinity], find the value range of real number a
• 2. lim f(x) = ln(x) / x x->0+ To do this
• 3. It is proved that LIM (x → x0) x & # 178; = (x0) &# 178;
• 4. LIM (x tends to 4) (x ^ 2-6x + 8) / (x ^ 2-5x + 4)
• 5. Calculate the limit LIM (below Lim is x → 2) x ^ 2-4 / x ^ 2-6x + 8
• 6. LIM (x tends to positive infinity) [x] * sin (1 / x) =?
• 7. Lim x tends to infinity 2 ^ n sin (x / 2 ^ n)
• 8. Mathematical analysis Lim n →∞ sin π / N = 0 It requires a definition~
• 9. Lim x ^ SiN x (x tends to 0 -)
• 10. How to calculate sin5 / 12 π × cos5 / 12 π? Please give the detailed process, thank you
• 11. Let f (x) = ln (x + 1) + ax, (a ∈ R and a ≠ 0). (I) discuss the monotonicity of function f (x); (II) if a = 1, it is proved that f (x) − 3 ＜ LX holds when x ∈ [1,2]
• 12. Given the function f (x) = x ^ 3, then when Lim △ → 0, (x + △ x) ^ 3-x ^ 3 / △ x What is (x + △ x) ^ 3-x ^ 3 / △ x equal to when seeking Lim △→ 0?
• 13. LIM (x → 0 +) lncotx / LNX is used to find the limit
• 14. Finding the derivative of (1 / LNX)
• 15. Using derivative to prove inequality: 0
• 16. 3.9 the solution set of inequality e ^ / LNX / > x ^ 2-2 is______ .
• 17. On the inequality e of X, the solution set of which X is greater than LNX is
• 18. It is proved that if the function f (x, y) is continuous on the bounded closed domain D, the function g (x, y) is integrable on D, and G (x, y) ≥ 0, (x, y) belongs to D, then at least one point (a, b) belongs to D, such that ∫ (domain D) f (x, y) g (x, y) d Δ = f (a, b) ∫ (domain D) g (x, y) d Δ = f (a, b) ∫ (domain D) g (x, y) d Δ
• 19. Let f (x) be differentiable in the interval (0,1) and f '(x) be bounded. It is proved that the series ∑ (n from 2 to infinity) [f (1 / N) - f (1 / (n + 1))] is absolutely convergent In the answer, [f (1 / N) - f (1 / (n + 1)) = f '(ζ) (1 / n-1 / (n + 1)) = f' (ζ) * 1 / N (n + 1),) absolute value f (1 / N) - f (1 / (n + 1)) ≤ M / N ^ 2, how does this m / N ^ 2 come from
• 20. It is known that the function f (x) is a differentiable function on (0, + ∞), if XF '(x) > F (x) is constant when x > 0 (1) It is proved that the function g (x) = f (x) / X is an increasing function on (0, + ∞) (2) When X1 > 0, X2 > 0, f (x1 + x2) > F (x1) + F (x2)