How to prove that the limit of x ^ 2 is 4 when x tends to 2 Especially that idea, how did you think of taking δ as that value

It can be proved by the limit of function

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1. It is proved that the limit x ^ 2 + 2x + 4 = 12 when x tends to 2 Proof by the definition of the limit of higher number function My proof process is that there exists ε > 0, so that | x ^ 2 + 2x + 4-12 | = | X-2 | x + 4|
2. Prove with the definition of function limit: limx ^ 3 (x tends to 2) = 8
3. 16. When x → 0, 2x + (x ^ 2) sin1 / X is the? A equivalent infinitesimal of X, B the same order but not equivalent infinitesimal, C the higher order infinitesimal, d the lower order infinitesimal
4. Let x → 0, etanx ex and xn be infinitesimals of the same order, then n is () A. 1B. 2C. 3D. 4
5. If x tends to 0, (1-ax ^ 2) ^ 1 / 4 and xsinx are equivalent infinitesimals, find a
6. When x → 0, (1-ax ^ 2) ^ (1 / 4) - 1 and xsinx are equivalent infinitesimals
7. When x approaches zero, (1-cosx / 2) is a higher order infinitesimal of X?
8. Let f (x) = (SiNx ^ 2 + 1), find the Taylor formula with Peano remainder of F (x) at x = 0, and find f (n) (0)
9. Think about the problem, to know cosx + SiNx = 1, find the nth power of (cosx) + (SiNx)=
10. The limit of cosx when x tends to π / 2 By the way, we also find the limit of cosx when x tends to zero I just learned the limit, I don't know anything. It should be proved by the limit's ε - δ formula
11. Let (2x-1) 7 = a7x7 + a6x6 + +A1x + A0, it is not necessary to find the value of X, then A0 + A1 + A2 + a3 + A4 + A5 + A6 + A7=______ ．
12. What is the square of minus A4? Is it the eighth power of negative a or the eighth power of a?
13. LIM (1 + K / x) to the x power, X tends to infinity, fast
14. Find limit LIM (x →∞) [(1 / x) + (x power of E)]
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16. What is the x power of e equal to a
17. How to calculate that the x power of e divided by the - x power of e equals 1 / 2,
18. 1. Find the limit (1 + X twice) open radical + x x tends to infinity 2, find the limit ((X-2) open radical - root 2) / ((2x + 1) open radical - 3) x tends to infinity 4
19. When x tends to 0, (root sign (1 + x) - root sign (1-x)) / X asks for the help of God
20. The fifth power of (3x + 5) = a (the fifth power of x) + B (the fourth power of x) + C (the third power of x) + DX & sup2; + ex + F, then the value of A-B + C-D + E-F is?