High school math problems, find detailed processes.

Derivative, the slope is -2, and the tangent equation is y=-2x+2 y=0 x=i, y=x and y=-2x+2 x=2 3 3 The height of the triangle is 2 3 The area is: (1 2) (2 3) 1=1 3 So you should choose a I hope it can help you Hope to be satisfied with the answer Thank you.

y=e^2x+1

y'=2e^2x

y(o)'=2

And because the tangent crosses the point (0,2), the tangent is y=2(x-0)+2=2x+2 tangent and y=o intersect the point (-1,0).

Intersect with y=x at the point (-2, -2).

As can be seen from the drawing, the area of the triangle = 1 2*1*2=1

In summary, the tangent of the curve at the point (0,2) and the triangle enclosed by the lines y=0 and y=x have an area of 1

Deriving the curve, we get the slope of the straight line: y'=-2*e -2x, bring (0,2) into it and get a slope of -2

The tangent equation obtained from the point oblique formula is y=-2x+2

Draw a picture. The area that can be counted is 2 3

Choose B and ask if you don't understand.

Option a analysis: first calculate the slope of the tangent of the curve, and multiply the derivative f(x)=-2 by the -2x power of e. Bringing in gives =-2 so the tangent equation is y=-2x+2

Then calculate the area, you draw the diagram with the y-axis as the base, the bottom length is 1, and the height is even if the x value of the intersection of y=x and y=-2x+2 is calculated to be x=2 3

So the area is s=1x2 3x1 2=1 3 If you are satisfied, hope.

Derivative slope: y'=-2*e^-2x

Bring in (0,2) to obtain a slope of -2, the tangent equation is y=-2x+2y=-2x, the intersection of y=x and y=x is (2, 3, 2, 3), y=-2x+2, and y=0 is (1, 0).

So triangle area = 1 2 * 1 * 2 3 = 1 3 will not be asked again. Good luck with your studies. Hope.

1) When a=2, f( )=丨2 +2|+1, the inequality f( )x<2 is:

丨2x+2|+1+x 2,丨2xten2丨<1-x, -1<2x+2<1-x,-3 So what you ask is:.

2), f(x) b10|2x Ten A |，b≤|2x Ten A |I|2x 10a 丨+1, let g(x) = 丨2x 10 a丨-丨2x 10 a l 10 1 solution set empty, there must be b g(x)ma ,g(x) 丨2x 10a 2x a 丨10 1

a a丨 ten丨, let h(a) = 丨 a a a丨 ten 1

The maximum value on a [a, 1, 3, 1] is.

h(a1 3) = 13 9, b (a, 13 9).

To classify and discuss A, there are five situations, see the following answers for details.

From the meaning of the title:

First of all, m>=0, is a natural number, m=0, get x=-5, which is in line with the meaning of the question: -5, 10 x is an integer (integer zero), y=0, then 10-x is a number that can be squared as an integer.

Then the set of x is [.]

Substituting the verification yields m

x = 6, m = 22 3 (round).

So m=(0,3,14,30).