Suppose that sin(a) = 4/8 and cos(b) =3/8 define in the first quadrant, determine sin(a+b). (round to 4 decimal places)

Q: 18. Evaluate ſe3 cos 2x sin 2x dx 1,3 cos 2x + C c.e3cos 2x + C B. -e3 cos 2x + C e3 cos 2x D. 6 sin…

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Q: 1 Show that L-1{ = (sin hat sin at) s4+4a4, 2a²

A: It is given that, L-1ss4+4a4=12a2sinhat sinat. A partial fraction decomposition of ss4+4a4:…

Q: 2.1 Given that sinh x = [e" – e=*] - - show that dy cosh a. da

A: To Determine: show that dydx=cosh x Given: we have sinhx=12ex-e-x Explanation: we have…

Q: sec(θ)=11/3

A: Please refer to the image below

Q: Q3) Ify = in[sec 8 + tan 8) find

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Q: d Select one: æ(sin=! æ)* 3x + 2 sin- x 3x x(sin x) -1 + 2(sin-1 x)? 1-a2 x² (sin-1 æ) 3(sin1 x) +…

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Q: 1) Match each function with its gray-Cos Cos x y = Sin x y=-Sin x y =-Cos x Slide correct function…

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Q: 10. Suggest ways to avoid loss of significance in these calculations. (1) Vx² +1-x; (3) sin x- tan…

A: 1 x2+1-x By rationalization  =x2+1-xx2+1+xx2+1+x=x2+1-x2x2+1+x=1x2+1+x Therefore, as x→+∞ there…

Q: Q#( 1b Compute: [cos (10x)sin²(10x)dx 1 sin°(10x) – A) 30 1 sin°(10x)+C 50 1 cos°(10x)- 1 -cos…

A: We have to solve the given indefinite integral

Q: 4. Find fyryzyaz, if f(r, y) = x² cos[100(e" + /1+ y²)®]

A: Given; f(x,y) = x2cos[100(ey+√(1+y2))y]

Q: 4. Evaluate 5 cos x dx 3 v2 sin x – 1

A: To evaluate : ∫π6π3 5 cos x32 sin x - 1 dx

Q: 6. Suppose you wish to differentiate g(x) = sin²(x)+cos²(x). What is the fastest way to do this, and…

A: Given,

Q: 4) state laylors your estima te 5) Using in Taylor's Theorem, show that the error in 3) for cos…

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Q: 1) If y = (x-a)√2ax-x² + + a is constant. x- -1(*-ª) ,then y' = 2√2ax - x² a² sin-¹ a²

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Q: 9 If f(0) = cos 01 cos 02· cos 03 ... cos On + tan 0,}=- f (0) Show, {tan 0, + tan 02 + tan 03 +…

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Q: 15 and x terminates in guadrant III. 17 Find sin2x, cos 2x, and tan 2x if sin x= - sin 2x cos 2x %3D…

A: The solution is given in the next step.

Q: 43. If > 2, then -dr = - 4 Jcos (4) + k B sin- ()+ k '(;) + A Cosh- (5) + k cosh=(4 D 2 tanh-(4) +k

A: for this integration, we will assume that x=sec(theta) and from that, we will solve the integration.…

Q: Sešx cos 8x dx 3x [8 sin 8x - 3 cos 8x] + C A) 73 B) 73 [8 sin 8x + 3 cos 8x] + C C) (8 e3x sin 8x +…

A: MULTIPLE QUESTIONS:   “Since you have asked multiple questions, we will solve the first question for…

Q: If e 17/2- 2i =sin2 then z = %3D - 2i In(sin2) + 4kn -2 In(sin2) + 4kT - 2i In(sin2) – 4kn 2i…

A: Concept : eiθ =cos(θ)+i sin(θ)                  if θ=2kπ                    ei2kπ =cos(2kπ)+i…

Q: (5) a) Find the linear and quadratic approximations of sin(0.967) tan(0.26) + (0.96)²(0.26) b)…

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Q: 8 and x terminates in guadrant III. 15 Find sin 2x, cos 2x, and tan 2x if tanx= sin 2x %3D cos 2x…

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Q: Evaluate: 8 sin xcos xcos 2.xdx -cos 2x- 1 cos 2x +C 10 8 cos 2x--cos 2x +C С. A. 14 1 -cos 2x 10 1…

A: Integration is generally used to calculate area under the curve. When function definition changes…

Q: 4 cos z Evaluate S 16-y2 ydxdydz

A: To solve the given triple integral ∫0π∫04cosz∫016−y2ydxdydz…

Q: 3. Give upper and lower estimates (in terms of n alone) for sin nb COs na + valid for all a, b; show…

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Q: 4. Differentiate the following. Justify ever (i) f(x) = (2x + 1)³(5x² + 4) (iii) sin(cos x)

A: Given function is: fx=2x+135x2+4 Differentiating f(x) with respect to x we get,…

Q: - Find the extreme value/s of f(x) = 4 sin² x cos 2x on (37 3π 5π 22

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: 32. a. b. f cos(4sinx - 1) cos(2sinx + 8) cosx dx is sin(6sinx + 7) − sin(−2sinx + 9) + C 1 1 12. 1…

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Q: 7). Suppose a is a positive constant less than T. Prove that the equation 2x+cos x = a has a real…

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Q: 9. To solve tek ₁ [theat] = 10. Let cos(√2t)]= you may use: n! (s = a)n+¹ II. [teat] = (-1){(f(t)}

A: Note: since you have posted multiple questions. As per our guidelines we are supposed to solve only…

Q: 5. Consider the equation: 3x – 2 cos x = 0. Use Newton's method starting with the initial…

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Q: 15 Suppose that tan a = TC <a<t. 2 and - Find the exact values of cos and tan 2 - JT Cos Undefined…

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Q: 9-10.j Show that sin20 2tane %3D 1+tan20

A: We will prove the trigonometric formula.

Q: x = Cịcos (At) + C2 sin (At)

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Q: 6. Suppose that < 0 < n and sin 0 = . Find the other 5 trigonometric functions evaluated at 0.

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Q: 6. Evaluate |2 Sin xʻdx, by (i) mid-point rule, and (ii) Simpson's 1/3 rule.

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Q: 4. Consider the problem of estimating a root of the equation cos(2x) - x = 0 via Newton's method.…

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Q: 8. Suppose that the tangent line to the graph of ƒ(x) = r0) at r = 1 is equal to the tangent line to…

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Q: Differentiate D = x2 + sin25x with respect to t and simplify. x2 + sin? 5x dt dt x2 + sin2 5x)1/2 dt…

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Q: 13 20 Find for Two only of the following: dx 1- y=xtanhx 2- y =cosh 3x- sinh²3x

A: We have to find derivative

Q: 2. Locate the first positive root of f(x) = sinx + cos(1 +x³)- 1 where x is in radians. Use four…

A: (a) We need to find the root between 1 and 3

Q: 9 If f(0) = cos 01 ·cos 02·cos 03 ....cos 0n %3D Show, {tan 0 + tan 02 + tan 03 + ... + tan 0,}=- f…

A: First note the results derivative of log x is 1x and derivative of cos(x) is -sin(x). The proof of…

Q: 9. Prove that | sin n0/sin 0| <n, limiting values being used when sin e = 0.

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Q: 3 Q19- if z =- 4x³y sin sin (x³y) əz find əx

A: We want to find partial derivative of the given function.

Q: 6. In right ALMN with right angle at N, sin L 4x-0.22 and the cos M 2x+ 0.28. Determine and state…

A: Given; sin=4x-0.22 and the cosM =2x+0.28.

Q: Show that, for real values of x, 3 sin x f(x) 2 + cos x cannot have a value greater than 3 or a…

A: To show that the minimum and maximum value of the function is -√3 and √3

Q: 16. So the maximum occurs at an angle of 0, but only if the angle is small enough. Explain why that…

A: Given: v=2μgscosθ+μsinθ Here μ is the coefficient of friction, g is the acceleration due to gravity…

Q: 5. Evaluate SO-2²πT ydx = 3π₁ given x = 0 - sine, y = 1- cos -0

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Q: 1. Determine the smallest positive root of f(x) = Sin x + Cos ( 1+ x ) - 1. Use 5 %3D iterations of…

A: Given function is f(x)=sinx+cos(1+x2)-1 the graph of the function is From the graph we can see that…

Q: 8. [Calculator Active] Find the least integer value n, such that T,(x)=1-+-++(-1)" - successfully…

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Q: 3 Differentiate: y = In cosh° (cos 2x)

A: As we know that: The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1 From the given problem:…