High number questions, about limits and derivatives, ask for detailed answers! I understand the addi

1. The formula you are seeking can be rewritten to the 1 n power of (1+n 2), for which you can use the second of the two important limits to rewrite, and the rewriting result is the n-squares of [(1+2 n)'s n 2nd power], and the limit result in the brackets is e, so you get the n-squares of e, find the limit for it, and the result is 1(Maybe I'm not very clear, but if you write down what I'm saying with a pen on paper, you'll understand.) ）

2. Since the derivative of f(x) is a continuous function above zero to positive infinity, then the integral of f'(x) exists, that is, f(x) exists.

Suppose (1+2 n) (1 n)=y, so lny=1 n*ln(1+2 n).

When n->0, 1 n->0, ln(1+2 n)->ln(1+0)=0, so lny->0

y->e^0=1

f(x)=integral[0,x] e y y dy +c This integral diverges at x-> infinity, so it does not exist.

Why divergence, when y>0, e y y>1

So f(x) > integral [0,x] 1 dy +c>x+c when x-> infinite, f(x) > infinite, so divergent, so does not exist.

1.The limit is 1

1+2 n is greater than 1 and less than or equal to 3

When n approaches infinity, the limit of 1 under the n root sign is equal to 1;

When n approaches infinity, the limit of 3 under the n root sign is equal to 1

Knowing by obsessiveness.

When n approaches infinity, at the limit time of (1+2 n) at the root sign of n times, 1

Here, since x is close to 0, it is substituted into the infinite power of 1, and if it is written in red pen in the figure, it can be concluded that the denominator numerators are all close to 0, and you can use Lopida to find the derivative.

f'(0)=lim(x 0)[f(x)-f(0)] x, which is the formula for defining the derivative at x=0.

Because it is derivable at the point of x=0, so f(x) is continuous at the point of x=0, so lim(x 0)[f(x)-f(0)]=0, so lim(x 0)[f(x)-f(0)] x is the limit formula of type 0 0, and the numerator and denominator are both derivable at x=0 point, using Lopida's rule, the numerator and denominator are derived at the same time, and it is obtained.

lim（x→0）[f（x）-f（0）]/x=lim（x→0）[f（x）-f（0）]'/x'

In the molecule, f(0) is a constant (the value of any function at any specific point is a constant), so the derivative of f(0) is 0

So the derivative of the molecule is f'（x）

The derivative of the denominator is 1

So lim(x 0)[f(x)-f(0)] x=lim(x 0)[f(x)-f(0)].'/x'

lim（x→0）f'（x）/1

lim（x→0）f'（x）

Test: BAI

First of all, b, can be excluded

The dud option zhi, the dao derivative is greater than zero, no matter how b, d will be selected, so it is excluded.

Among the remaining options A and C, if A is correct, C must also be correct, and vice versa, because it is a multiple-choice question, only C is selected.

Knowledge Points:The derivative of a point is greater than zero and does not lead to a monotonic increase in the decentering domain of that point, as follows:

But the derivative of a point is greater than zero, which can be proved by the definition of the derivative and the number preservation of the limit to prove that option c is true:

First, you need to figure out what you want to do in graduate school. Most people think that the goal is to find a good job, so if you can find your dream job after graduating from bachelor's degree, you can consider working for a few years first, and then go to graduate school when you want to recharge. If you can't find a suitable job for the time being, you may wish to consider studying for graduate school first.

Secondly, you have to consider your own strength, after all, there will be some conflicts between going to graduate school and finding a job. If you think you have enough strength, you might as well make a two-handed preparation and find a job at the same time as the graduate school entrance examination.

Finally, I think the economic power of the family is also an aspect that I should consider. If the financial situation does not allow it, it is better to work first.

Hopefully, the above tips will help you!

1, because the left and right limits of the derivative are not equal. x-a+, -ln3, x-a-, ln32, take the logarithm of the left and right sides, and find the derivative.

3, the same as 2 practices.

4. Add the term f(x0), use the definition of the derivative to split, f(x0+a n)-f(x0) form, and the denominator is written as a n, then multiply by n a, this is the definition of the derivative, and the same is true for the second term. (1 a-1 b) Derivatives of nf(x0).

5. Draw a picture to see that it is continuous, and the left and right limits are equal, which proves it.

But it can't be derived, and the derivatives are not equal. Write a segmental function, find a derivative, and prove it.

It's not difficult, do it slowly.

The third step is wrong.

Because f is not said in the title'0 must exist.

The premise of the limit four operation is that the limit must be ensured.

So the third step lim(f+g) ≠ lim f+lim g (because the limits of f and g do not necessarily exist).

<> profit is defeated and used f'The dry smile of (0) defines the stove car type.

<> Ming banquet is ready to destroy the silk white.