Answer to Solving High Numbers Masters please enter !!!!

I just won't tell you I won't do ==

It's a matter of finding the limit.

It is necessary to consider whether the limit exists.

<> "In Problem 6, =y is the integral factor, and multiplying this factor on both sides of the equation makes the original equation a full differential equation. 】

2.Attestation Arctana-Arctanb A-B

Proof: without losing generality, set a>b

As the function y=arctanx, which is continuously derivable in the interval [b,a], so according to the median theorem, there is:

arctana-arctanb=(a-b)f'( b< y=arctanx is an additive function, so f'(0, obviously, arctana-arctanb>0;.)a-b>0；f'(ξ0;

0 when a then there is an inequality: 0>arctana-arctanb a-b, both sides multiplied by -1, the inequality sign is reversed, which is equivalent to the absolute value of both sides. i.e. there is arctana-arctanb a-b

1 2ln(x 2+y 2)=arctany x, two-sided differentiation, 1 2*[(2x+2ydy dx)]*1 (x 2+y 2)=[(xdy dx-y) x 2]*[1 1+(y x) 2], you can get the result after sorting, or use the formula dy dx=-fx(x,y) fy(x,y)fx(x,y) means to find the partial derivative of x. f(x,y)=1 2ln(x 2+y 2)-arctany x=0.

I don't know how to express this symbol. But if you treat x as an independent variable and y as a dependent variable, you can just find the derivative of x on both sides, but it really doesn't work, look at the references, and look through similar questions, and you will understand.

I'd also like to know the answer, I was going to derive both sides at the same time, but I calculated the value of x.

Let f(x)=e x-x-1

f‘(x)=e^x-1=0

When x=0 is obtained, f(x) obtains the minimum value.

So f(x)> f(0)=0

i.e. e x> x+1