Find the function y = root sign (1 + x), when x0 = 3, △ x = - 0.2 change amount △ y

Find the function y = root sign (1 + x), when x0 = 3, △ x = - 0.2 change amount △ y

△y=f(x0+△x)-f(x0)
=f(3-0.2)-f(3)
=f(2.8)-f(3)
=√3.8-√4
=√3.8-2
=-0.05...

Find the derivative (1) y = X-1 (2) y = root X of the following function at x = x0 (x0 ≠ 0)

Y '(x0) = LIM (f (x + x0) - f (x0)) / [(x + x0) - x0] = limx / x = 1 x - > 02, y' = 1 / 2 radical x, y '= 1 / 2 radical x0 at x = x0, y' (x0) = LIM (f (x + x0) - f (x0)) / [(x + x0) - x0] = LIM (radical (x + x0) - radical x0) / [(x + x0) - x0] = li

The function f (x) = 4sin to the second power X + 4root 3sinxcosx-3 is known
1. Find the minimum positive period of F (x)
2. Find the monotone increasing interval of F (x)
3. If. X belongs to {0, π / 2}, find the maximum and minimum of F (x),
(process, thank you)

f(x)=4(sinx)^2+4√3sinxcosx-3
=2(1-cos2x)+2√3sin2x-3
=2√3sin2x-2cos2x-1
=4(√3/2sin2x-1/2cos2x)-1
=4(sin2xcos(π/6)-cos2xsin(π/6))-1
=4sin(2x-π/6)-1
therefore
1. The minimum positive period of F (x) is 2 π / 2 = π
2.f(x)=4sin(2(x-π/12))-1
So the difference of monotonic increase is [K π - π / 4 + π / 12, K π + π / 4 + π / 12]
That is [K π - π / 6, K π + π / 3] K ∈ Z
3. When x ∈ [0, π / 2]
f(x)=4sin(2x-π/6))-1
Obviously, in - π / 6

If the axis of symmetry of the ellipse is the coordinate axis and the sum of the length of the major axis and the length of the minor axis is 18, the coordinate of a focus is (3,0)
Find the standard equation of ellipse

x^2/a^2+y^2/b^2=1
The sum of major axis length and minor axis length is 18
2a+2b=18.（1）
The coordinates of a focus are (3,0)
C = radical (a ^ 2-B ^ 2) = 3. (2)
The solution is: a = 5, B = 4
x^2/25 + y^2/16 = 1
or
16x^2 + 25y^2 - 400 = 0

It is known that the symmetry axis of the ellipse is the coordinate axis, the length of the long axis of the ellipse is 3 / 2 times of the focal length, and the length of the short axis is 8 √ 5
Find the elliptic equation

There are two solutions to this problem: a = 3 / 2C, 2b = 8 √ 5 and A2 = B2 + C2
We can get a = 12, B = 4 √ 5, C = 8
When the axis of symmetry is on the X axis, the equation is x2 / 144 + Y2 / 80 = 1
When the symmetry axis is on the Y axis, the equation is x2 / 80 + Y2 / 144 = 1