(3) Proving that sin?(x) + cos (x) = 1: d. (a) Show that -(cos² (x)+ sin (x)) = 0. What does the constant function theorem d.x tell you about sin?(x) + cos²(x)?

Q: A-f cos (x)sin³(x)dx e*cosh (3x) B-J cosh(x)+sinh(x)

A: Here we use use substitution method to evaluate the given integral.

Q: If e 2i =sin2 then z = = sin2 = 2 - 2 In(sin2) + 4kT 2i In(sin2) + 4k TI - 2i In(sin2) – 4k T | - 2i…

A: Given that, e-z2i=sin2e-z2i=sin 2e-z2i×ii=sin 2eiz2=sin 2

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Q: 1 lim h-0 2h sin(x²)dx = %3D -2h O cos(1) sin(1)

A: Using Fundamental theorem of calculus: ∫-2h0sin(x2)dx=sin(0)-sin((-2h)2)=0-sin(4h2)=-sin(4h2)

Q: 1. f(x) = sin 2x + cos 3x + x² = 0 with xo = -0.5 , Ax 0.1, TOL = 0.001, in [-0.5,1] %3D

A: Given equation is fx=0 where f(x) is defined by fx=sin2x+cos3x+x2  Given initial solution is x0=-0.5…

Q: cos 2x–1 lim COS х— 1 cos x-1

A: limx→0cos 2x-1cosx-1

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Q: 2. f(x) = x²cos 2 x 3. f(x) = tan x – sec x sin x 4. f(x) = 5. f(x) = 2cos (2 + x³) 6. f(x) = x²ln x…

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Q: 36. (a) Prove the reduction formula 1 cos"-'x sin x + п S cos"x dx = | cos"-2x dx n n (b) Use part…

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Q: エ→2 x² -4 1- cos 2x 7) lim X sin x エ→0

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 5cos³(x) sin(3–2x) answer in terms of sin and cos only ind the derivative of y = + tan²(3x² – 4x) –…

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Q: cos 2x dx is (sin x+cos x) -1 A. sin x+ cos.x +C B. log sin.x+ cos.x +C C. log|sin.x-cos x| +C 1 D.…

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Q: f cos(x³) x² dx. O 1 ¹ cos4 + c 4 1 3 sin x²+ C 1 1 ¹ cos4 + c - 4 -3 si sin x³+ C

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Q: x2 – 1 - if x <1 x – 1 - f(x) = T In x a cos 2rx + b sin(- 4 In 2 if 1<x < 4 if 4 < x where a and b…

A: Explanation of the answer is as follows

Q: lim h-0 2h sin(x² )dx = -2h cos(1) sin(1)

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Q: The derivative of cos (x²) Graph y = -2x sin (x²) for –2 < x < 3. Then, on the same screen, graph…

A: We draw the graph of y=-2x*sin(x^2) using graphing calculator

Q: Evaluate cos x + 2 cos³ x + 1 dx cos' x cos4 x 7 +x + c 2 sin7 x sint x +x + c cos x +x + c 3. cos X…

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Q: (-1)° x*1 (2k –1)! 2k-1 k=0 a) sin x b) cosx c) sin x- x d) cosx-1 e) e* ||

A: Given,

Q: ( (cos(2r) – sin(2x)cos(2x)) -dx =. For +C. What is F (x)? cos(x) – sin(x)

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Q: 1-T= 3- Z= +cos(y)tan ( √x-b cos (n) 2-sin²(n) 2-B=sin(x) sec(x)/cscf(x) 4-(w+n)²(a+) x-3

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Q: a . Show that y = sin x, y = cos x, and y = a cos x + b sin x (a and b constants) all satisfy the…

A: a. Given

Q: x3 + x2 ) lim x→-1 x+ 1| (i) ( 3 Vx2 +x +6+ Vx + 8 - 5x (ii) 6) lim x1+ x2 – x (iii) ( sin(3x)…

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

Q: 9. The value of f 1-x 1+x A. sin ¹¹x + √1 + B. sin¹x - √1 + dx x² + C x² + C C. sin ¹¹x + √1- x² + C…

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Q: 3x2 sin(x³) Select one: а. In/tan x3 + cot x³| + c b. -In csc x3 + cot x³| +c С. с. In|sec x3 +tan…

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Q: Apply Newton's Method to f(x) and initial guess xo to calculate x₁, x2, X3. f(x) = cos(x) - 11x, xo…

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Q: (x²-2 (a) f(x) = 4, (sin 2x x + 2 (b) f (x) = { 1, x-2 at x = 2. at x = 0. X = 2 x = 0

A: A function is continuous at any point x=a if it satisfies the below condition. LHL=RHL=fa LHL is the…

Q: 4. Express the function f(x) = 11 sin x +7 cos x as a function in terms of sine. Express your answer…

A: To find 11sinx+7cosx in terms of sine function only.

Q: This problem deals with functions defined by f(x) =x + b sin x, where b is a positive constant and…

A: Given,   f(x)=x+b sin x  y=x+b :-Tangent to f(x)

Q: sin a COS T Solve by hospital rule lim-

A: after solving we get limit is 1/3

Q: 3. Use Newton's Method to approximate the positive zero of f(x) = e* – 2 cos(x). Xo = 0 X1 = X2 = X3…

A: Answer is below

Q: 4. Find the absolute maximum and absolute minimum of the function f(x) = 3 sin(x) cos(x) over the…

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Q: sin(bx)+a x<0 f(x)=< | sin (2x)+2x x20 which is differentiable everywhere, then what are values of a…

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Q: 6. Approximate the real root of x – cosx = 0 to three decimal places. Let xo = 0.8 and find x1, x2,…

A: Let f(x) = x - cos(x) x0 = 0.8 By using the Newton-Raphson method to approximate the root,…

Q: 6. The value of A. sin ¹¹x + √1 + x² + C B. sin-¹ x - √1 + x² +C C. sin-¹ x + √√1- x² +C D. sin…

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Q: 50. Find a real root of f(x) =x sin.x+ cos x = 0 by Newton Raphson method.

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Q: 5. Evaluate | (x² +1)* dx using trigonometric substitution as your first step (not a u-sub as your…

A: The solution is given below in the next step:

Q: 2. Let f(x) = -x³ - cosx and po = -1. Use Newton's method to find p2. Could po = 0 be used?

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Q: x²+1° w(x) = arctan x²-1, f. g(x) = ln (x³ – ) - g. f(0) = sin(sin(sin(0)))

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Q: = sin? (esin" t) + cos-1(2t3 (x) = tanh-1 x + In V1– x2 |

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Q: X+1 1-x Select one: a. sin-1(x)-V1-x² +c www. O b. sec-(x)-V1-x? + c C. tan (x)-V1-x2 + C d. cos x)…

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Q: 4 sin x cos x + 2 sin x - 2 cos x - 1 = 0

A: first factorize the given equation and than split two product equation  detailed solution is given…

Q: - sin²( a Find the equation of the line tangent to f (x) = cos² x – - sin° at x =

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Q: Q-1: Integrate the fraction of functions: 1. f- 14a+1 2. sinx- V(1-x) 2-7x-4x2 dx 3. SE 1-sine dep.…

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Q: Scos“ x- sin' xdx x•sin³ xdx 3

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Q: 2x² sin (x²)dx = V(1-x*) Select one: a. - sin-(x²) cos(sin(x²)) + x² + C b. - cot-(x?) sec(sin-(x²))…

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Q: The value of A. sin-¹ x +√1+ x² + C B. sin ¹x-√√1 + x² + C C. sin-¹ x + √1- x² + C D. sin¹x-√1- x² +…

A: The  given integral is ∫1-x1+x dx The trigonometric identity is expressed as sin2θ+cos2θ=1 therefore…

Q: cos 2x-cos 4.x Express f(x) = using factor formulae. Hence, determine sin 2.x + sin 4x dy of y =…

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Q: 3 Find the maximum and minimum values for f(x) = - 4-(/2 cos x - V2 sin x)

A: Topic = Functions Maximum value of f(x)=1.5 Minimum value of f(x)=0.5

Q: 5. y = tan-¹tan x] ab 6. f(x) = x² cos-¹¹-√x²-1 7. f(x) = tan ¹(sin² (2x)) 8. y = (cot ¹(sin¹(x))³

A: