If sin(x + y) – sin(x – y) = 2f(x) sin y, then f(x) is equal to C. tan x D. cos? x A. sin c В. cos x

Q: Sco The value of cos (x+3) dx with U=x+3 is -cos (x+3) sin(x+3) +C -cos(x)+c

A: The given integral is ∫cosx+3dx.

Q: Find the general solution for = sec x + y tan x y' A. y = sin x + c cos x В. у %3D csc x + с cot x…

A: Recall: First order differential equation : Given the first order differential equation…

Q: If S (x) = - sin(x), then f (11) (x) is equal to – sin(x) B B -cos(x) CosX sin (x) D O cos(x) A,

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Q: Consider x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? 1/2 1/4 3/8

A: We have given  ∫x sinx cosx =fx sin2x-gx cos2x+C Let,  I=∫x sinx cosx dx I=∫x sin2x2dx I=12∫x sin2x…

Q: Consider x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? 1/2 3/8 1/4

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Q: Differentiate y= e*cos (x²): y = A e(cos(x?) – 2xsin(x?)) B -2xe"sin(x?) (c) e*cos(x²) – 2 xsin(x²)…

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Q: (23) If f(x) = sin zx, find the value of fe (x). 23 sinx %3D 23 e. sin x a. 23 b. cosx . 1 cos TEX…

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Q: :? If sin(x +y) = xy, what is the correct expression for dx cos(x+y) - y x- cos(x+ y) A cos(x + y) -…

A: for this problem, we can solve this by using general implicit  differntiation.

Q: The coefficient of Sin(x) in the antiderivative of F(x) =| cos is 17/16

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Q: 4. Given f(x)= sin 6x cos 6x dx , what is f| | if f(0)= x ? A. π В. О С. 2л D. — я

A: This integration can be integrated by using substitution method. Clearly it is observable that put…

Q: If f(x) = 5 sin x + 12 cos z, then %3D f'(x) = f'(2) =

A: The question has been solved in detail in the next step.

Q: If f (x) = – sin(x), then f (10) (x) is equal to A - sin(x) В - cos(x) C sin(x) D cos(x)

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Q: 2 cos x dx, 1+ sin x (c) t = sin r. 0.

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Q: 4- Find dy/dx for: a- y = sec?x – tan?x b- y = sec³ ( – x) %3D c- y = sin(tan(3x)) d- y = /1+ sin³…

A: NOTE- Since questions 1, 2, 3, 5 and 6 are incomplete, so solving question 4 only. Please submit the…

Q: x sin (x²) cos(x²), from a = 0 to b = x 2

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Q: Q1- Find the root of the functions within ɛa < 4 % f(x) = e-*(3.2 sin(x) – 0.5 cos(x)) Given that x…

A: According to the given information, it is required to find the root of the function.

Q: If f (x) = – sin(x), then f (11) (x) is equal to A -sin(x) B - cos(x) © sin(x) D D cos(x) B

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Q: Determine whether ƒ is even, odd, or neither.

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: given f (x) = 3/5 cos (6x), what is the smallest possible value for f (x)?

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Q: Find the root of f(x) = e −x (3.2 sin(x) − 0.5 cos(x)) on the interval [3, 4] up to 1 d.p.

A: Consider finding the root of f(x) = e-x(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

Q: 15. For fe' cos x dx, what is du? cos x e' dx - sin x dx G(e* cos x + e" sin x) + C

A: The given question can be solved as shown in step2.

Q: If f(x) = 2 sin x + 12 cos x, then f'(x) = f'(3) = %3D

A: Given functionf(x)=2sinx+12cosx thendifferentiate with respective…

Q: For the function f(x) = sin x , with the aid of elementary formula sin2A = 1/2 (1 − cos 2A), show…

A: Given that fx=sinxfx+y=sinx+yfx+y=sinx cosy+cosx siny by addition formulaNow ,       fx+y-fx…

Q: d) f(x) – e) f(x) = sin [In (x² - 3x)] sin x f(x) = 1+COS X

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Q: The general solution of sin (x)-cos-(x)3cos(x) is: a. x=2km b. x=TT+2kTt, x=±+2KTT c. X=2kt, x=±+2ka…

A: Given  sin2x-cos2x=cosx Use trig identity sin2x+cos2x=1…

Q: -sin x 0 [cos x - If f (x) = | sin x - 0, show that f(a)f (b) = f (a + b). 1] cos X %3D 0. 0.

A: Given: Here, f(a)=cosa-sina0sinacosa0001, f(b)=cos b-sin b0 sin bcos b0 001. Now,…

Q: For S* sin x dx, what is dv? sin x dx OA 2x dx - cos x+ 2x sin x+2 cosx+C O.

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Q: Find (f −1)'(a). f(x) = 4x3 + 5 sin x + 2 cos x,    a = 2   (f −1)'(a) =

A: Consider the function f(x) =4x3+5sinx+2cosx.Compute the derivative of the given function as follows

Q: c) f(x)=tan(cos².x) 11 COS X 1+ sin.x Dy=- b) y = 2

A: e)  f(x)=tan(cos2x)  f) y=cosx/(1+sinx) g) y=ex^2/x3 Repost the next part.

Q: f(x) = 2 sin x + 8 cos x, then f'(a): f'(x) = f'(5) = |

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Q: 12. Given that V3 cos x = cos(-x), tan x= A 3. cos(f B V3 C 1. V3

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Q: 2 tan 4x dx The is equal to 1- tan 24x A. In(sec 8x) + C B. In(sec 8x)8 + C 1 C. In(sec 8x) + C D.…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: 13. Find the general solution = sin x + y cotx. a. y = (x + c)(secx + tan x) b. y = (x + c) sin x C.…

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Q: Find the points of inflection,smaller x-value,and larger x -value  of the graph of the function. (If…

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Q: If y = sin (sin x) and d dy tan x + f(x)= 0, then f(x) equals dx2 (A) sin² x sin (cos x) (C) cos? x…

A: Introduction :

Q: Given f(x) = x² +3 sin x+2 cos x. Find (f-ª) (2).

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Q: 2. For the function f(x) : = sin x. Show with the aid of the elementary formula. 1 1 (1- cos 2A)…

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Q: The function f(x) = sin(kx) contains the point A(, -1). The function is: Oa) f(x) = sin(-x) Ob)…

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Q: If f (x) = - cos(x), then f (0)(x) is equal to A - sin(x) B - cos(x) В © sin(x) D cos(x)

A: We have to differentiate the given function 9 times

Q: (5) Find the local extreme values of the function h(x) = sin?x – V2 . sinx + 2/2 on the interval (0,…

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Q: 1. Given sinx 12 and cos y : 13 both x and y lie in sxs, determine a) cos(x+y) b) sin 2y

A: Given query is to find cos(x+y) and sin2y.

Q: For sin y=- find the value of so that (y+y")= - 1 at 1 at x=0 Cos X-

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Q: If f(x) = 6 sin x + 12 cos x, then f'(x) = f'(4) = %3D

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Q: If y= cot"+ tan-1x?), then dy dx x2 Select one: 2х + 1+x*' 1-x4 2x O a. 2x O b. 1+x' 1+x? 2x Oc. 2x…

A: All given options are wrong. See the attachment

Q: 1 The function (x) = x sin x satisfies the following equation: f"(x) + f(x) + t cosx = 0. The value…

A: solve the differential equation

Q: The f sin x cos x dx is not equal to {A} -cos 2x + C {B }sin'x + C {c}-cos'x + C {D} sin 2x + C

A: Given query is to find the incorrect option for the integral.

Q: Find W (ex, cos x COs x sin x). B.) -2 (e) sin x cos X

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Q: 3 The value of (Isi n(x)| + x²) dx is .a 2 f(- sin(x) + x²) dx 0 .b .C 2 f(sin(x) + x²) dx -3 .d 3 ,…

A: Let's find.

Q: y = tan x sin (2x)+cos (2x) 2 y' = A sin (Bx) + Ccos(3x) 3. A = B = C =

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Determine the ABSOLUTE EXTREME values of the function y = cos x + sin x, over the interval 0<x < 2T

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