![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
How to understand lobida's law?
When the numerator denominator tends to infinity or infinity, it's difficult to calculate their ratio. This is to use lobida's law to derive the numerator denominator at the same time, and it's easy to calculate after inversion
How to prove lobida's law There is only 0 / 0 proof in the book Who helped me give me 8 / 8 proof? Take the inverse transformation to 0 / 0, and the form of upper and lower derivation is different from that of 8 / 8.
Dy / DX - > k, X - > 8 can get (1 / dy) / (1 / DX) - > k, X - > 0. So the problem turns into 0 / 0
When X - > 8, f (x) / g (x) = (1 / g (x)) / (1 / F (x)) = D (1 / g (x)) / D (1 / F (x)) = f (x) * f (x) * G '(x) / (g (x) * g (x) * g' (x))
=>f(x)/g(x)=f'(x)/g'(x)
Lobida's law What is the meaning of 0 / 0 and infinity in the lower lobida law? For example, why doesn't Lim x approach 0 (x + cosx) / x?
At this time, cosx tends to 1
Molecules do not conform to infinitesimal
Application of lobida's law
Lobida's law is a common and effective method for solving indefinite forms or limits in mathematical analysis. The flexible use of lobida's law is also the embodiment of our own mathematical problem-solving ability, which has important application value. This paper briefly analyzes the definition, concept and theoretical basis of lobida's law, through more than ten examples, This paper focuses on the application of lobida's law in solving limits and proving problems in mathematical analysis
Lobida's rule is an effective method to solve the "0 / 0" and "∞ / ∞" limits. When using lobida's rule to solve the limits, only pay attention to the following three points:
1. Before using lobida's law every time, it must be verified that it is "0 / 0" and "∞ / ∞" limits, otherwise it will lead to errors;
2. Lobida's law is to find the derivative of numerator and denominator respectively, not the derivative of the whole fraction;
3. If the result obtained by using lobida's law is a real number or ∞ (no matter how many times it is used), the result of the original limit is this real number or ∞, and the solution is over; If the final limit does not exist (not in the case of ∞), it cannot be asserted that the original limit does not exist, and other methods should be considered
Find the limit limx - > 0 (SiNx / x) ^ (1 / x ^ 2) Given is e ^ (- 1 / 6),
Natural logarithm first
limx->0ln（sinx/x)^(1/x^2)
=Limx - > 0 (lnsinx LNX) / x ^ 2 (this is type 0 / 0, using lobida's law)
=limx->0(cosx/sinx-1/x)/2x
=limx->0(xcosx-sinx)/(2x^2sinx)
=limx->0(cosx-xsinx-cosx)/(4xsinx+2x^2cosx)
=limx->0-xsinx/(4xsinx+2x^2cosx)
=limx->0-sinx/(4sinx+2xcosx)
=limx->0-cosx/(4cosx+2cosx-2xsinx)
=-1/6
So limx - > 0 (SiNx / x) ^ (1 / x ^ 2) = e ^ (- 1 / 6)
Limx → 0 + (SiNx) ^ x limit Find the limit with Robida's law,
Take logarithm
ln (sinx) ^x
=xlnsinx
=lnsinx/ (1/x)
Robida's law
= cosx/sinx /(-1/x ²)
= -x ² cosx/sinx
=【-2xcosx+x ² sinx】/cosx
=0
So original restore
=e^0
=1
RELATED INFORMATIONS
- 1. It is proved by definition that when x tends to 1, LIM (3x + 2) = 5
- 2. Find LIM (x → 0) (SiNx / x) ^ (cosx / 1-cosx)
- 3. Note the functions F1 (x) = f (x), F2 (x) = f (f (x)),... FN (x) = f (f... F (x)), and the intersection of the definition fields of these functions is d. if any x belongs to D Note that functions F1 (x) = f (x), F2 (x) = f (f (x)),... FN (x) = f (f... F (x)), the intersection of these function definition fields is d. if any x belongs to D, all n values satisfying FN (x) = f (x) constitute a set P, and all n values satisfying FN (x) = x constitute a set Q. (1). If f (x) = 1 / x, find sets P and Q, (2). For function f (x) = ax / (x + B) (a ＜ 0), 2 belongs to Q, find the relationship between a and B
- 4. Given that the definition domain of function f (x) is [0,1], find the definition domain of function g (x) = f (x + m) + F (x-m) (M > 0)
- 5. How much more is the quotient of the reciprocal of 7 divided by 6 than 1 / 5 of 25 You cannot use a segment calculation
- 6. [(- 3xy) square times x to the 3rd power - 2x square times (3xy Square) cube times Y / 2] divided by 9x to the 4th power y to the 3rd power Followed by y to the power of 2
- 7. Prove that | SiNx | is less than or equal to | X| Classified discussion, using derivative method.
- 8. The square of X + 1 = x (x + X part) is this factorization
- 9. The sixth power of X - the sixth power of Y + the fourth power of X + the square of X, the square of Y + the fourth power of Y,
- 10. It is known that the - x power of (1 / 3) is equal to one-third of the - y power of 2 and 3, equal to 5, and find the value of 2x-y power of 9
- 11. On the problem of de centring neighborhood in Higher Mathematics When learning advanced mathematics, I encounter a problem: The neighborhood can be represented by {x | a - R < x < x + R} Then, if point a is removed, it becomes a de centered neighborhood, which can be expressed as: {x | 0 < | X - a | < R} I just can't turn around now. Why can I see | X - a | < R at a glance? Although I know that | X - a | < R is definitely right, I can't see it at a glance and ask for advice
- 12. Urgent! If the function f (x) is differentiable at x = 0, and f (0) = 0 x tends to 0: then find the limit f (x) / x =?
- 13. Differential mean value theorem problem It is known that f (x) is second-order differentiable on [a, b], a (a, f (a)), B (B, f (b)). Line segment AB intersects y = f (x) curve at another point C. verification: existence μ ∈ (a, b), so that the second derivative f '' (x) = 0, there is no reward,
- 14. 2. Among the eight numbers 3, 4, 5, 6, 7, 8 and 9, the sum of any four numbers is multiplied by the sum of the other four numbers, and () different products are obtained?
- 15. Three natural numbers add or multiply to get the same result. What are the three numbers? thinking
- 16. Multiply any two numbers from - 6, - 4, - 3, - 2, - 1,3,6, and record the maximum value as a and the minimum value as B. what is the value of a / D
- 17. Find the limit limnsin (2 π en!) (n - > ∞)
- 18. Limx → 0 ln (2-x ^ 2) - LN2) / cosx-1 limit
- 19. Limx → 0 ∫ cosx is the limit of negative T square / x square of the lower limit and 1 is the upper limit E. (detailed process.) thank you
- 20. 1. Calculate the generalized integral ∫ [0, + ∞] DX / (100 + x ^ 2). 2. Find the monotone interval of function f (x) = x ^ 2-lnx ^ 2