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Find the value range of function f (x) = 2 (SiNx + cosx) + sin2x-1
f(x)=2(sinx+cosx)+sin2x-1 =2√(sin2x+1)+(sin2x+1)-2 =[√(sin2x+1)+1]²-3∵0≤sin2x+1≤2∴0≤√(sin2x+1)≤√2∴1≤√(sin2x+1)+1≤√2+1∴1≤[√(sin2x+1)+1]²≤3+2√2-2≤[√(sin2x+1...
Given the vector M = (2sinx cos, SiNx) vector n = (cosx SiNx, 0) and f (x) = (M + 2n) m (1), find the minimum positive period of function f (x) (2) By shifting the function f (x) to the left π / 4 units, the monotone increasing interval of G (x) is obtained
(M + 2n) = (cosx, SiNx), (M + 2n) * m = (2sinx-cosx) cosx + SiNx = 2ssinx cosx-cos-s (x + SiNx) x + sin = sin2x-cos2x = sin2x-cos2x = sin2x-cos2x = sin2x (2x-π / 4) therefore, f (x) = √ 2Sin (2x - π / 4) minimum positive cycle T = π g (x = f (x + π / 4) minimum positive cycle T = π g (x = f (x + π / 4) - f (x + π / 4) - π / 4) = √ 2Sin [2 (x + π / 4) - π / 4] = √ 2Sin (2x (2x (2x / plus
Given the vector m (cosx, - SiNx), vector n (cosx, sinx-2, radical 3cosx), X belongs to R, Let f (x) = m * n + 2, Given vector m (cosx, - SiNx), vector n (cosx, sinx-2 root sign 3cosx), X belongs to R, Let f (x) = m * n + 2, find the minimum value of function f (x); 2. If f (x) = 50 / 13, and X belongs to [π / 4, π / 2], find the value of sin2x. 3. Let the inequality f (x) > = 3 hold. 4. If the equation f (x) = K (0)
Problem 1: so f (x) = (cosx) ^ 2 - (SiNx) ^ 2 + 2 radical sign 3sinxcosx + 2
=(cos2x + 1) / 2 - (1-cos2x) / 2 + radical 3sin2x
=Cos2x + Radix 3sin2x
=2 * (1 / 2cos2x + radical 3 / 2sin2x)
=2 * (sin30 degree cos2x + cos30 degree sin2x)
=2 * sin (2x + 30 degrees)
Because x belongs to R, there is a minimum value of 0 when x = 5 π / 12 + K π
There's another question I don't have time to answer, but it seems to be a senior one or from last semester?
If x ∈ [π / 6, π / 3], then the value range of the function f (x) = 2cos? X + sinx-1 is?
0-1
The value range of function f (x) = 2cos ^ x + sinx-1, X ∈ [0, π / 2]
Substitution method
Let SiNx = t,
∵ x∈[0,π/2]
∴ t∈[0,1]
∴ f(x)=2cos²x+sinx-1
=2-2sin²x+sinx-1
=-2sin²x+sinx+1
=-2t²+t+1
=-2(t-1/4)²+9/8
When t = 1 / 4, f (x) has a maximum value of 9 / 8
When t = 1, f (x) has a minimum value of 0
The value range of F (x) is [0,9 / 8]
Given the function f (x) = a (2cos ^ 2x / 2 + SiNx) + B, when a = 1, find the monotone increasing interval of function f (x);
B = a (1 + cosx + SiNx) + B = a (1 + cosx + SiNx) + B = a (1 + cosx + SiNx) + B = a (cosx + SiNx) + A + B = √ 2A (sin π / 4cosx + cos π π / 4sinx) + A + B = √ 2asin (π / 4 + x) + A + B + B + B + monotone increasing interval is [2K π + 3 π / 2-π / 4, (2k + 1) π / 4, (2k + 1) π / 4, (2k + 1) π + π / 2-π / 4] that is: [2K π + 5 π / 4, (4, (2k π / 4), (2k π / 4), (2k π + 5 π / 2K + 1) π + π / 4]
Let f (x) = SiNx radical 3cosx, X ∈ R (1) find the minimum positive period of F (x) and (2) find the monotone increasing interval of F (x)
f(x)=sinx-√3cosx=2sin(x-π/3)
So period T = 2 π
From 2K π - π / 2
Find the minimum value of the function y = SiNx + 2sinx · cosx + 3cosx and the set of X with the minimum value, and find its maximum value
(2x + π / 4) when 2x + π / 4 = 2K π + π / 2) when 2x + π / 4 = 2K π + π / 2, there is a maximum value of 2 + √ 2, x = k π + π / 8, K ∈ Z, when 2x + π / 4 = 2K π + π / 2, K ∈ Z, when 2x + π / 4 = 2K π - π / 2, K ∈ Z, when 2x + π / 4 = 2K π - π / 2, K ∈ Z, when 2x + π / 4 = 2K π - π / 2, X = k ∈ 2, x = k ∈ 2, x = k ∈ 2, x = k ∈ 3 Z
Find the tangent equation of the curve X ^ 2 / 3 + y ^ 2 / 3 = a ^ 2 / 3 at the point ((root 2) / 4 A, (root 2) / 4A)
The original equation is a circle equation, (root 2) / 4A, (root 2) / 4A) is a point on the circle, so the tangent passing through this point is perpendicular to the straight line from the center of the circle to this point, and the center of the circle is (0,0)
So the first line is y = x, the slope of the line is 1, the slope of the tangent is - 1, so the tangent equation is: y = - x + √ 2 / 2A
Find the tangent equation and normal equation of X at point m (1,1) under the curve y = f (x) = cubic root
y=x^1/3
y`=1/3x^(-2/3)
k=y`(x=1)=1/3
y-1=1/3(x-1)
y-1=-3(x-1)
RELATED INFORMATIONS
- 1. Tangent equation and normal equation of X + 1 at (1.2) under y = root sign
- 2. The function y = asin (ω x + φ) + m (a > 0, ω > 0, | φ| π) is known 2) Its maximum value is 4, its minimum value is 0, and its minimum positive period is π 2, the line x = π If 3 is a symmetric axis of the image, then the analytic expression of the function satisfying the condition is______ .
- 3. The known function f (x) = Cos2 ω x+ The minimum positive period of 3sin ω xcos ω x (ω > 0) is π (I) find f (2) 3 π) (II) find the monotone increasing interval of function f (x) and the symmetric axis equation of its image
- 4. F (x) = 2 radical 3sin (3wx + Pai / 3) (W greater than 0) (1) if f (x + Z other) is an even function with period 2, find w and Z other values (2) f (x) is in (0, Pai / 3) F (x) = 2 radical sign 3sin (3wx + Pai / 3) (W greater than 0) (1) if f (x + Z other) is an even function with period 2, find w and Z other values (2) f (x) is an increasing function on (0, Pai / 3), and find the maximum value of W
- 5. The absolute value of Radix X-2 plus Radix 2-x plus 2y-1 is equal to 5. What are x and y
- 6. If the straight line y = KX + 1 and the curve X = radical y ^ 2 + 1 have two different intersections, then the value range of K is
- 7. How to simplify √ 3cos ^ x + sinxcosx - √ 3 / 2 to sin (2x + π 3)
- 8. What is the increasing interval of the function y = 1 / 2Sin (2x - π / 6)? What is the period? What is the amplitude? What is the phase shift?
- 9. The graph of the function f (x) = ︱ x + 3 - ︱ x-3 ︱ is drawn and observed. The monotone increasing interval and monotone decreasing interval are pointed out
- 10. The function y = 2Sin (2x − π) 6) The monotone decreasing interval of is______ .
- 11. Y = the range of | SiNx | - 2sinx? When SiNx ＞ = 0, y = ｜ SiNx ｜ - 2sinx = - SiNx, the range is [- 1,1] When SiNx < 0, y = - SiNx - 2sinx = - 3sinx Why is the value range of the final answer: [- 1,3]?
- 12. Let f (x) = m vector × n vector, where vector M = (2cosx, 1), n vector = (cosx, √ 3sin2x), X belongs to R In the triangle ABC, a, B, C are the opposite sides of angles a, B and C respectively. We know that f (a) = 2, B = 1, and the area of triangle ABC is √ 3 / 2. We can find the value of B + C / SINB + sinc
- 13. If + F (x) is a even function (- F, x) = 0, then (f) (x) is equal to (- 0, f) = 0=
- 14. If y + 2 is an increasing function, then x = 2 is an even function A、f（1）＜f（5/2）＜f（7/2） B、f（5/2）＜f（1）＜f（7/2） C、f（5/2）＜f（7/2）＜f（1） D、f（7/2）＜f（1）＜f（5/2） The process is because f (x + 2) is an even function, so the axis of symmetry of F (x) is x = 2. Why is the axis of symmetry x = 2?
- 15. Let y = f (x) be an even function defined on R, and its image is symmetric with respect to x = 2. When x ∈ [- 2,2] is known, the function f (x) = - x ^ 2 + 1, then when x ∈ [- 6, - 2], f (x)=
- 16. Derivative of high school mathematics known function f (x) = ax ^ 4 + BX ^ 3 + CX ^ 2 + DX + e is even function The tangent equation passing through point a (0. - 1) and at x = 1 is 2x + Y-2 = 0. Find the analytic formula of y = f (x)
- 17. If f (x) satisfies 2F (x) + F (- x) = 3x + 2, then f (2)=________ ? Can you carry two numbers at will, for example: 2f（2）+f（-2）=8 2f（-2）+f（2）=-4 Then, the equations are solved to obtain f (2) = 4
- 18. It is known that the minimum positive period of the function f (x) = sin 2 Wx + root sign 3sinwxsin (Wx + half π) (W > 0) is π 1. Find the value of W, 2. Find the range of values on the interval [0,3 / 2 π]
- 19. Known a＝(− 3sinωx，cosωx)， B = (COS ω x, cos ω x) (ω > 0), Let f (x) = a• b. The minimum positive period of F (x) is π (1) Find the value of ω; (2) Find the monotone interval of F (x)
- 20. Given the function f (x) = LG [(a ^ 2-1) x ^ 2 + (a + 1) + 1], if the definition field of F (x) is r, then the value range of real number a is? Given the function f (x) = LG [(a ^ 2-1) x ^ 2 + (a + 1) + 1], if the definition field of F (x) is r, then the value range of real number a is? E, that one has an X