Suppose /s(x)dr f(x) = sin(4-). Evaluate: (A - 3cos (B -cos

Q: Compute cosh x and tanh x, assuming that sinh x = 0.8.

A: Here given as sinhx=0.8 Use the identity…

Q: [In(x²)-ex cos(x-1).tan(Tx) 20. lim 2x2-x sin2(1-x) X-1

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Q: (b) Prove that : - 1) (coshx)2 – (sinhx)2 = 1 ,2) coshx- sinhx = e-*, 3) (cothx)? -1= (cschx)?

A: Given that  The following

Q: 5. Show that cos (sin 2x) + sin (cos-1 2x) = (V2-2x)(VZ+2x) -

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Q: |2tan x In (cos x) dx=

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Q: 7. Show that sin E + x) = G+x): = -cosx.

A: Introduction :

Q: 5) Integrate 2x cos (x²-5) with respect to x.

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Q: Express in exact form: In(x² + 1)dx

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Q: What do the limits limh→0((sin h)/h) and limh→0((cos h - 1)/h) have to do with the derivatives of…

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Q: 4. Evaluate sin (44°) + COS (290) using differentials. Refer to special triangles.

A: To evaluate  sin440+cos290 using differentials.

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 & cos-1x

Q: Differentiate implicitly cos(x³y³) = 9

A: Given,         cosx3y3=9

Q: 2tan x In (cos x) dx=

A: here we have to integrate the given integral.

Q: 1- Prove that cosh 2x - sinh 2x = e2

A: sol)Given cos h 2x-sin h 2x=e2x

Q: Determine a root of f(x) = 2* +3 cos(x²)-2 with 10-3 accuracy.

A: Given :f(x)=2x+3cosx2-2

Q: Find the derivative of cos(3x) O -3sin(3x) O 3sin(3x) O 3cos(3x) O -3cos(3x)

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Q: -sin (In x?)ecos² (In x) dx 100x2-x2e2 cos (In x)

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Q: 7. The derivatives of the function f (x) = cos(3x²) that follow are incorrect. What misconception…

A: The differentiation of product two functions can be calculated by using the formula,…

Q: Obtain graphically an approximate value of the lowest root of cos x cosh x =- 1.

A: The equation cosxcoshx=-1 regulates the frequency of vibration of a cantilever. We must first…

Q: Differentiate y = coS 7 + sin4x+ x cos x + 4 with respect to x. 1. 2.

A: the given function is: y=cosπ+sin-1(4x)+xcos(x)+4x3 we have to differentiate the given function with…

Q: 2 cos(5x) – 5 x² – 2 lim sin(3x) – x² – 3x - - (Write your answer in the given box)

A: We will use L'Hopital rule

Q: 4. Show that sinx can be approximated by x-x³/6 within 0.01 on the interval [-1,1].

A: see my solution

Q: If f(x) Files = Time left 0:5 sin²x and g(x) = 1 + cos²x, how are f'(x) and g'(x) related? Maximum…

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Q: If f(x) = COS X then f' (x) equals: X S0)- -sin x cos X:

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Q: f'(t) = sin 8t - cos -/-

A: You are correct

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: 31. Verify the formulas sinh-x = In |x + Vx² + 1| coshx = In |x +Vx² – 1| (for x > 1)

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Q: Find the smallest positive zero of f(x)=cos^2(x)-sin^2(x)

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Q: If f(x) = 2 tan '(5 sin(3r)), f'(x)-

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Q: Evaluate. de (sin(5x – 1)] cos(5æ – 1) 5 - sin(5æ – 1) 5 · cos(5æ – 1) • 5· cos(x)

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Q: 4. Prove that cos(sin¬1 x) = /1 – x².

A: cos(sin-1x)=1-x2⇒sin-1x=cos-1(1-x2)Let y=sin-1x                               (1) ⇒siny=x…

Q: 3- - 플 플 sin²cyl y จน

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Q: If f (x) = - cos(x), then f (10) (x) is equal to (A) - sin (x) ® -cos(x) © sin(x) D cos(x)

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Q: 4. Ify =/sin x+ /sin x+.to inf inity, dy _ cosx dx 2y-1 prove that

A: Derivative of Sinx is Cosx

Q: x sin 2x sin COSX 8. Prove that: %3D 2x-7

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Q: 7. Find the derivative with respect to x of tan-(2) – In(2.r +3) = 4 cos (2y +5). %3D

A: To find the derivative of tan-1x2-ln2x+3=4cos32y+5. Solution: Power rule of differentiation states…

Q: 15. -- sin(2+ 2) dz

A: According to the given information, it is required to solve the give integral.

Q: Find , if da y = 3x cos4x 12x* sin4x – 10x cos4x None -2x4sin4x – 12x° cos4x -12x4 sin4x + 12x°…

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Q: Prove cosh 2 x - sinh 2  x =1

A: To prove  cosh2x-sinh2x=1

Q: do sin 0 – cos 0 cos 0

A: The given integral is ∫dθsinθ-cosθ

Q: cos(9x) -dx COS J 1+ sin²(9x)

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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: when

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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: 2. 1 Given: cosh x==(e* + e*), =(e* - e**), use these sinh x = definitions to show that cosh²x-sinh2…

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Q: Evaluate ax xm-1 sin bx dx in terms of Gamma function. -ax

A: We use the special results of Gamma function to solve this problem as in next step.

Q: 6. Show that in the interval (0, 7) 4 cos 2nx sinx = 元 Σ 4n2 -1

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Q: Differentiate the following functions 4 1-cos2x Y = by chain rule. 1+cos2x

A: To differentiate the given function.

Q: Given the function y = 6 cos(3x + 1) The second derivative y" %3D Select one: 18 sin (3x + 1) -18…

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Q: Compute f sin(cos(x²)) sin(x²)x dx

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