Infinitely smaller than the order (1.47-1.63)

2020 1000 Tommy title · a · number of brush title record

The first chapter of Higher Mathematics

Chapter 1 limit, continuous

Second, infinitely smaller than the order (1.47-1.63)

1. Alternatively equivalents order determined by several, (. 5> n-+> \. 3. 1) \ , calorific value of a positive integer.
2. After unreasonable denominator of surprise, \ (TaNx-SiNx \ SIM {\ FRAC. 1} {2} {X ^}. 3 \) .
3. Infinitely small amount of interaction, to see that the minimum order.
4. Taylor normal replacement or equivalent, expand principles, formulas and can not take the lowest that x is 0, then the order.
5. ? ? ? Why xlnx not a infinitesimal?
   \ (xlnx = x [(1 + x) - \ dfrac {1} {2} (1 + x) ^ 2 + o (x ^ 2)] \ sim x ^ \?)
6. Original order when x is infinitesimal formula, so the original formula / x ^ k limit exists. (And it usually is not 0)
7. \ (\ Alpha '= cos \ x ^ 2 \ sim o (x ^ 0); \ quad \ beta' = 2x \ tan \ sqrt {x ^ 2} \ sim 2o (x ^ 2) \ quad \ gamma ' = \ {1} {2 dfrac \ sqrt x} \ sin \ {\ sqrt x} ^ 3 \ sim \ dfrac {1} {2} o (x ^ 1); \)
8. Error practices: \ (\ Lim \ limits_ {X \ 0} to SiNx (cosx-. 4) + 3x \ SIM (X-\ {dfrac. 1} ^ {X}. 6. 3) (1-4) + 3x = \ dfrac . 1} {2} {X ^. 3 \) ,So 3 infinitesimal.
   Taylor directly after expansion (two each expanded) by multiplying the sum, or by multiplying the Taylor expansion (each deployed three) are added, and finally all low-level x have been eliminated, leaving only a higher order of x (if left a number of words, to see that the minimum number of items x).
9. (1) Extraction \ (\ SQRT2 \) out to the \ ((1 + x) ^ \ alpha -1 \ sim \ alpha x \) against the upper. (2) (3) two equivalents may be substituted.
10. To \ (x-sinx \) rely on two \ (sinxcosx = \ FRAC. 1} {2} {sin2x \) .
11. With 1.44 looks a bit like, but not the same type. Taylor expansion directly, erasing 1, the minimum order is taken to x, the original formula ~ 7x ^ 2. The second answer is too much trouble, as well? ? ? Why \ (sinxcosxcos2xcos3x = \ dfrac. 1 {{}}. 4 sin4xcos3x = \ dfrac. 1 {{}}. 8 (sin7x-SiNx) \) .
    It is used and the difference between the product of the trigonometric function formula, and additionally also review the differential equation of the plot:
12. Extraction and equivalents may be substituted.
13. Ibid., Extraction and substitute equivalents, to \ (e ^ x-1 \ sim x \) against the upper.
14. Derivative and equivalents may be substituted.
15. \ (LNA = LNB-LN \ dfrac {A} {B} \) , then split and equivalents may be substituted \ (\ lim \ limits_ {f (x) \ to 1} ln [f (x)] = \ lim \ limits_ {f (x) -1 \ to 0} ln [1 + f (x) -1] \ sim f (x) -1 \)
16. Split and equivalents may be substituted.
17. The kind of feeling do math college entrance examination, the calculation of trouble, but it worked out so cool. Clarify the meaning of the questions before the drawing, and then build a formula based on known conditions, then the unknown with the formula expression. Finally, according to the same order, on behalf of the retention limit + order.
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One thing to note, the serial number of the original 47-63 display properly VNote, posted to the blog page into a park 1-17. = =