Example. Let T 3T , such that {0, 4 2 Rx - 4 Find E[sin(X)].

Q: 1. sin xsin ydx+cos x cos ydy = 0 2. dr = b(cos Odr+rsin Ode) 3. x cos² ydx + tan ydy = 0

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: The function g(x) = n + 0.5 sin () has a fixed point on [0, 2 1]). Select one: True False

A: Fixed points of a function f(x) are the solutions of the equation f(x)-x=0 if f(x) is defined on the…

Q: (Example P.2) Defihe: G: R'-> R sin G), ifx#0 ifx= 0 by: 1.02 Glx) = { %3D Does G'lo) exist ?

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Q: A. cos (T – n1) n=1

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 2. Graph the function f(x) = cos(2x) +1. %3D

A: y=cos2x+1 to graph the function, we need a few points x y=cos2x+1 -2π 2 -7π4 1 -3π2 0…

Q: The domain of the function f(x)= cos( - 5) is [A,18] k Then A +k =.

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Q: a. Let f (x) = sin (ax + b) and let g (x) = cos(ax + b) where a and b are constants. Gues a formular…

A: We have to find the f^n(x) and g^n(x)  Where f(x)= sin(ax+b)  and  g(x)= cos(ax+b)

Q: 5. Select all that are true. ха хв xaxb = xa+b (xa)b = xab sin² 0 + cos² 0 = 1 √2 2 T √2

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Q: Let h(z) tan(5x + 5). Then h' (2) is and h'' (2) is

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Q: Let f(x)=2x-3,g(x)-5x, and h(x)=x2 what is the sinpliest fornm of h(x)*g(f(x))

A: Explanation of the solution is given below...

Q: S(x)=sin(xx), g(x)=x² -x

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Q: a. Let f (x) = sin(ax + b) and let g (x) = cos(ax + b) where a and b are %3D constants. Gues a…

A: A function f is said to be continuous in the open interval (m, n), if it is continuous at each point…

Q: [3] Let f(x) = –x³. find p2, P3, and p4. Cos x and po = -1, pi = 0. Use the Secant method to

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Q: If g(x) = 5x and f(x)=4+cosx then find (fog)x and ( fog) x.

A: This question is taken from the derivative in which we have to find the composite function and…

Q: - PROBLEM For any real numbers C1, C2, ..., Cn show that n S COS | CRT₁(x) dx = [] cos CA. k=1 k=1

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Q: y = x cos(In x)+x² In x²

A: d dx(cosx) = -sinxddx(lnx) = 1xddxx2 = 2x   Product rule u.v = u'.v + v'.u

Q: Q5: Example. Let Rx {0, 4 2 4 * *} such that %3D Find E[sin(X)].

A: Given that RX=0,π4,π2,3π4,π To find: EsinX

Q: 6. y = C, cos x + C2 sin x + C3 cos 3x + C4 sin 4x ; C1, C2, C3 and C4 are arbitrary constants

A: The given equation is, y=C1 cos x+C2 sin x+ C3cos 3x+C4sin 4x Differentiate this equation up to the…

Q: If L{cos(ax)} then find L{x³ cos(ax)}. %3D p2+a²

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Q: 3.(1) Show that (x) - J{«) )x cos 2.x

A: Consider the Bessel function, Jnx=xn2n Γn+11-x222n+2+x42·42n+22n+4-…             ...1 Substitute…

Q: az a2z az a2z at ax2 23. If z = sim(x+ sint), show that дх дх дt

A: Given,Z=Sinx+sintto prove∂z∂x·∂2z∂x∂t=∂z∂t·∂2z∂x2

Q: 1)1, e*, e2*, e3* 2) 1, e*, xe*,x²e* 3) 1, sin x , sin 2x 4) 1, sin x , cosx 5) 1, cosx, cos2x O A)…

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Q: The Function f(x) = sin( 4* ) + sin( 4 *) is Select one: O An even Function O An odd Function O…

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Q: 1/a (e) lim (1– sin(z))/=

A: When limit is of the form 00 or ∞∞ , then L'Hospital rule is used.In this rule, we take the…

Q: Find a function of the form y = A sin(kx) + C or y = A cos(kr) + C whose graph matches the function…

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Q: 3-26 · Evaluate the integral. 3. (x cos 5x dx

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Q: Find values of a and b for which cos (ax) – b -1. lim x→0 2x2

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Q: If g(x) = cos(x) then = (2),6 g'(1) =

A: Given that, g(x)=cos (x)

Q: If g(x) = sin(x) then = (1),6 g'(1) =

A: Given function is g(x) = sin(x) we need to evaluate the derivative of function and value of…

Q: -1 -1 18. Show that cos (-x) =T- cos x

A: We have to prove that cos-1(-x) = π - cos-1x

Q: F. Find y' of each of the following: 3 x cos y+ y³ – xe' - 0

A: Taking derivative of given curve implicitly with respect to 'x' and using product rule of derivative…

Q: Suppose w = where ¤ = e", y = 2+ sin (3t), and z = 2+ cos (7t). %3D A) Use the chain rule to find de…

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Q: A. Find y' if 1. y = x² cos² 3x

A: y=x2cos23xApply product rule to differentiate the given function y with respect to…

Q: Q if asinx Prove that a + bcos X y' = (a+ bcosx)? a cos+ b

A: Differentiate wrt x In problem, proof equation is wrong I have solved properly

Q: az az and ду Ql:- Find the if Z = x4 sin x y³. Əx

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Q: f₁(x) = 9, f₂(x) = cos²(x), f3(x) = sin²(x) linearly dependent linearly independent

A: Here given  functions are.  9. ,Cos2x  , sin2x

Q: Find all functions ult, x) that Solve: where and u(0,2) =0 , 2u co,a) >e²

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Q: e* (1 + sin x de. nx] Evaluate 1 + cos x

A: I am attaching image so that you understand each and every step.

Q: lim e 0 t/ Select one True False

A: limx→0+e1xusing chain rulelet f(x) =1xg(u) =eulimx→0+ f(x) = limx→0+ 1x =∞

Q: iv) Evaluate fsin' x cos² x dx .

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Q: f(x) = a cos(bx) а cos

A: Given,                         f(x)=acos(bx)+cx+dif a=6, b=0.5, c=3 and d=4.

Q: Let a be a constant. Evaluate 2 ((2* + 2² + a) sin(4x³) + 12a²)dx.

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Q: Homework: 1. If y=tan x, prove that y`= 2(y +1)(3y² +1).

A: As per the guidelines I solve your first question. For more solutions please resubmit the question.…

Q: 2- Exercise: Evaluate a) L{4x? – 3 cos(2x) +5e*} b) L{4+sin (x) – e**}

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Q: f(x) - 7 еxp[cos (3х)]

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Q: 1 - T <x< T Ans. 4 cos(x) +cos(2.x) - 4 1 ***+ (xɛ)soɔ- 4) f(x) = 12

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Q: What is x sec xdx ? A. xtan x- In cos x+ C C. xtan x- In |secx+C | B. xsecx-secx tan x+C D. xsec x+…

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.