The known function f (x) = ax & # 178; - x + 2a-1 If a > 0, let g (a) be the minimum value of F (x) in the interval [1.2]

The known function f (x) = ax & # 178; - x + 2a-1 If a > 0, let g (a) be the minimum value of F (x) in the interval [1.2]

The axis of symmetry is 1 / (2 * a);
If 1 / (2 * a) 1 / 2, the minimum value is f (1) = g (a) = 3 * A-2;
If 1=

Find the maximum value of function f (x) = √ 1 + SiNx + √ 1-sinx + √ 2 + SiNx + √ 2-sinx + √ 3 + SiNx + √ 3-sinx

Here a > = 1ga2 (x) = 2A + 2 √ (a ^ 2-sin2x) when SiNx = 0, the maximum value of GA ^ 2 (x) is 2A + 2A = 4A, that is, the maximum value of GA (x) is 2 √ a, so the maximum value of F (x) = G1 (x) + G2 (x) + G3 (x) when SiNx = 0, is 2 + 2 √ 2 + 2 √ 3

Given that an original function of F (x) is SiNx / x, the integral of XF '(2x) is obtained

Let f (x) = SiNx / X. since LIM (X -- 0) SiNx / x = 1, f is defined on R. Let f (0) = 1 prove that f is differentiable at 0. By using the law of lobida (Taylor formula), we can get LIM (X -- 0) (f (x) - f (0)) / (x-0) = LIM (X -- 0) (SiNx / x-1) / x = LIM (X -- 0) (sinx-x) / x ^ 2 = LIM (X -- 0) (cosx-1) / 2x

If an original function of F (x) is SiNx, why f (x) = (SiNx) "

X = 45 degrees

If f (x) is an original function of SiNx, then all functions of F (x) are?

A:
F (x) is the original function of SiNx
Then f (x) = - cosx + C
So: all functions of F (x) are - cosx + C, where C is an arbitrary constant

The primitive function of SiNx / x,

If you really want to use the knowledge of progression
SiNx / x = sum sign (upper limit positive infinity, lower limit n = 0) (- 1) to the power of N, X * x to the power of 2n-2 / (2n-1)!
Then it's hard to get a phone call

Given the function f (x) = 2Sin (3 / KX + 4 / Pie), the period of F (x) is in (3)
(2 / 3, 4 / 3), find the minimum positive integer value of K

2/3

Given the function f (x) = 2Sin (KX / 5 + pi / 3) (k is not equal to 0), find the maximum and minimum value of the function and the minimum positive period; find the minimum positive integer k,
When the independent variable x changes between any two integers (including the integer itself), at least one value of the function is m and one value is m

f max=2
f min=-2
T=10pi/|k|
T=10pi/|k|=10pi
k=10pi
The minimum positive integer is 32

If the period of the function f (x) = 1 / 2Sin (KX / π + π / 4) is within (2 / 3,3 / 4), then all the desirable positive integer values of K are?

For y = asin (Wx + φ), the period T is only related to W, t = 2 π / W, for: 2 / 3

Given the functions f (x) = asin (KX + π / 3) and φ (x) = bcos (KX - π / 3) + 2011, K & gt; 0, their minimum positive periodic sum is 3 π / 2,

That is 2 π / K + 2 π / k = 3 π / 2
So k = 8 / 3
therefore
f(x)=asin(8x/3+π/3)
φ(x)=bcos(8x/3-π/3)+2011