This is a senior number problem in freshman year. We use the pinch theorem to find the limit  

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• 1. A high number problem, the use of the pinch criterion LIM (1 + 2 ^ n + 3 ^ n) ^ (1 / N) where n tends to infinity, why is its size between 3 and 3 times 3 ^ (1 / N)
• 2. Such as the title, with the pinch theorem! Please prove LIM (x → 0) Tan (x) / x = 1 with pinch theorem
• 3. The pinch theorem proves that the limit of a ^ n / N! Is zero Please prove that a ^ n / N! When n - > + ∞, the limit is zero
• 4. Using pinch theorem to find limit Find the limit of LIM (2x [3 / x], X tending to 0, where [x / 3] represents the integer function of 3 / X
• 5. The pinch theorem is used to find the limit, Xn=(A1^n+A2^n+…… +AK ^ n) to the power of N, where a1 > A2 > >Ak>0
• 6. lim(x→0)lncos2x/lncos3x Using equivalent infinitesimal to calculate
• 7. When x → 0, Lim {lncos2x / lncos3x} = Lim {(lncos2x) '/ (lncos3x)'} = Lim {2tan2x / 3tan3x} The specific steps of (lncos2x) '= 2tan2x
• 8. LIM (x tends to 0) ((e ^ x) * sinx-x (1 + x)) / x ^ 3 is solved by Taylor's theorem
• 9. Using Taylor formula to find the limit of [cosxln (1 + x) - x] / x ^ 2 and [e ^ x-x (1 + x)] / (x ^ 2 * SiNx)
• 10. When x tends to 0, SiNx arctanx is used to find the limit
• 11. How to take the values on both sides of the pinch theorem of higher numbers?
• 12. If f (x) = {xsin1 / x + B x > o a x = 0.5 + x ^ 2 x
• 13. Xsin1 / x + B, x0? ）What are the values of a and B, f (x) has a limit at x = 0? (2) what are the values of a and B, f (x) is continuous at x = 0? & nbsp; the more detailed the steps, the better
• 14. Lim e ^ x-e ^ SiNx / Tan ^ 2xln (1 + 2x) (x tends to 0)
• 15. How to do LIM ((TaNx SiNx) / x ^ 3) x - > 0
• 16. LIM (x → 0) (tanx-x) / X3 is the answer 0? PS please see clearly that the molecule is tanx-x, not TaNx SiNx in common questions My own way is: the original formula = LIM (x → 0) (tanx-x) / tanx3 =LIM (x → 0) ((1 / TaNx Square) - X / tanx3 Square) =LIM (x → 0) (1 / xsquare - X / x3) = 0 I don't know if it's right,
• 17. lim (x^2sin1/x) /sinx
• 18. When x tends to zero, five times SiNx, one-third equals zero
• 19. Find Lim [x ^ (n + 1) - (n + 1) x + n] / (x-1) ^ 2 x -- > 1
• 20. lim（x+x^2+…… +x^n-n）/(x-1)