f(x) = 0, if 0 < x <1 [-1, 1]); f(r) ~ - ao + > an coS + b, sin n=1

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: Given: y = x - sin(2x) Find: dy dx 0 - cos²x 2 ○ - sin² x 01+ cos²x O sin²2 X

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Q: nd all values of x in the interval [0, 2x] that satisfy the equation. (Enter your an 9 sin(2x) = 9…

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Q: Solve the following equation; 2 tanh- 2r = In(r – 2) – In(x). %3D

A: We solve this following equation using simple mathematics and its solve in a simple form of…

Q: 2. Without specifically finding its roots, show that f(x) = 0 for some x E [1, 2] where x2 4 f(x) =…

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Q: Solve for the value(s) of x over the interval 0 < x < 360 2 cos x + 1 = 0 %3D

A: We have to find values of x over the interval 0&lt;= x &lt;= 360 of the equation 2 cos (x) +1 =0.

Q: Use Secant method with p, =1, p =1.2 to find the root of f(x)= ln x – cos x that is accurate to…

A: Solution:Let f(x)=log(x)-cos(x)a=1, b=1.2, f(a)=-0.5403, f(b)=-0.2832Here f(a)&lt;0 and f(b)&lt;0.…

Q: -1 We can conclude from the derivative of sin-1(x)and cos-1(x) that sin-(x) + cos¯(x) is constant.…

A: Explanation: find the derivative of sin-1x &amp; cos-1x

Q: (3х' - 4х- 3) x* – x' +x² – -* dy = cos ydx – - 1- sin? y y

A:

Q: 3. Given f(x) = 2 In x – tan x, find f'(x). %3D -

A: we know that  ddx|nx=1x and ddxtanx=sec2x

Q: 2. Given: cosh x==(e²+ e*), sinh x=(e-e), use these 1-1/1 definitions to show that cosh’x−sinh’x=1.

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Q: Find the extreme values for f(x) = sin(x) + cos(x) on the interval [0, 2π].

A: The given function is f(x)=sinx+cosx   and the interval is 0, 2π. We have to find extrema on the…

Q: Find the extreme values of the function f(x) = sin(2x) within the interval 0 < x < 2n %3D

A: Given function f(x)= sin(2x)            0≤x≤2π

Q: Evaluate 1 ei sin x cosx dx using Simpson rule with h = 20

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Q: Find the solution of (tan x – sin æsiny) dæ +cos xcosydy = 0

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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: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…

A: The detailed solution is given below Thank you

Q: Evaluate D3(sinx – 4e) A cos x-32 ex B -cos x-32 e?x -sin x-32 ex sin x-32 e2x

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Q: a. Solve for real x, in the equation sinh 2x – 2 cosh 2x + 2 = 0. b. Express tanh x in terms of e*…

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Q: S cos ( x^3 ) dx = * sin ( x^3) + c 3x^2 sin (x^3 ) + c - sin (x^3 ) + c - 3x^2 sin ( x^3) + c none…

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Q: Let ( f(x)=cos(x)+2xe^x ) Use the secant method for finding the biggest negative root. Conduct two…

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Q: 5. If cosh 2x then the positive value of 4 sinh 2r is

A: Here we will use the relationship betweencosh2x and sinh2x to find the value of sinh2x from the…

Q: Find the critical numbers for the function f(0) = 2 cos 0 + sin? 0 for 0 < 0 < 2T.

A: A critical number of the function f is s number c is the domain of f that either f'(c)=0 or f"(c)…

Q: f(x)=X +Sin -1 く(-2)- 4-て+Sini-て)-\no9651 3(x)=てメ+ cosx ずし-て) ニ -4ACOS(-て)-3 (x)-2-らinx f(-2):…

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Q: The approximation of the root x* of the function f(x) = x sinx-1 accurate to within 10-2 using…

A: Introduction: Newton's method made use of the tangent line to the curve of y = f(x) with the point…

Q: Solve for the value(s) of x over the interval 0 < x< 360 sin(2) = - V3

A: values=?

Q: . Estimate the root of the expression, f (x) = x² – cos x, using: d. MOSS using xo = -1 with error…

A: As per the question we have to find the root of the equation : f(x) = x2 - cos(x) = 0 With tolerance…

Q: Find the root of f(n) = 3x - cos(x) -1 = 0

A: Please rate and feel free to ask any query about any part.

Q: Find an approximate solution, accurate to 5 decimal places, to the equation cosx=x2 that lies in the…

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Q: Find the x-coordinates of the points of inflection of k(@) = sin (e) on the interval 2 Use exact…

A: h(θ) = sin2(θ)  [ -π/2, π ]

Q: Suppose that the tangent line to the graph of f(x) = x(6*) at r = 1 is equal to the tangent line to…

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Q: V3 f. sin(2x) 2 tan(x) = 1

A: Solve the problem within the domain first find the inverse and then solve.

Q: 1) If f(x)= tan(5x), find  f'(5)=??????

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: The suitable substitution to evaluate sin 4(x+2) dx is None OA [1-cos8(v+2)] В. [1+ C. 2 + cos8(r…

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Q: Find the linear approximation of f(x)=sin(x) at x=3π4 and use it to approximate sin(134∘). Give…

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Q: 4. Find all solutions to the equation 4sin x cos x = v2 in the interval [0,2]

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Q: a. Solve for real x, in the equation sinh 2x – 2 cosh 2x +2 = 0. b. Express tanh x in terms of e*…

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Q: 9. Find the value of k so that (2y sin x cos x - y+ 2y²e")dx - (x- sin? x+ kxye*)dy = becomes exact.…

A: To find the  value such that given equation is exact  differential equation.

Q: 7. Over the domain 0s x s2n, the equation cos(x)-sin(x)%3D2 cos(2x) has:

A: We find the solution in the following way by using trig identities.

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: Find the extreme value/s of f(x) = 4 sin² x − cos 2x on . (³347) 3π 5π 2' 2

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Q: Where does the periodic function f(x) = 2ešin (x/2) take on its ex- treme values and what are these…

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Q: 6. Using a suitable substitution in each case, integrate the following w 1 (a) x2 + 10x + 29 sec?,…

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Q: To approximate the solution to the equation sin(2x – 1) = 0.7 using - Newton's Method, you find the…

A: To find the solution to any equation of the type g(x)=a, we need to apply Newton's method to the…

Q: (1) f(x) = {"x, r0, if - 2<x<0 х, if 0<xs2 O F«) = { 0, - n<x<0 0 <x<n sin x,

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Q: 5. Find the PARTICULAR SOLUTION: y' = 1+ 3y tan x when x = 0 ; y = 1

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Q: If f(x) cos-¹(2x+5), then dom(f) = = x+3 (A) (-3,-2) (B) [-3, -2] C)(-3,-21

A: