-Prove that: y" = 1 if y=csc(tan")

Q: Separate tanh-1(x+ iy) into real and imaginary parts.

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

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

Q: Find the exact value. In 3 0 ³ sech 4 x tanh x dx

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Q: 4) Estimate tan (0.5) using the tangent line to y = tan(x) %3D 6

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Q: Evaluate sin (44º) + cos (29º) using differentials. Refer to special triangles.

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Q: a if y = In (sinh 50) and x = 7. cosh 40

A: We have given y and x and we have to find out dy/dx

Q: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

Q: Find integral.

A: Given: Let I=∫2x cos x2 dx To Find: To evaluate the given integration.

Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: tan zeecz coS z

A: Integration is the process of finding the anti-derivative function of the given function.…

Q: 5) Evaluate the integral: tan 3 x dx

A: Given integral, ∫tan3x dx

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

A: To evaluate  sin440+cos290 using differentials.

Q: f(x)% 3D tanh In(2x) is equivalent to

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Q: Use Simpson's rule with n = 4 to approximate cos(x) dx 1

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Q: 29.Verify that W[xλ cos(μ ln x), xλ sin(μ ln x)] = μx2λ − 1.

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Q: If y- sinhx then prove that = dx

A: Fundamental inverse Trigonometric Identities: →cosh2y - sinh2y = 1 Basic derivative:…

Q: 1. Differentiate the function. y = In(VT sin-(5æ))

A: As per our guide lines we can answer only 1 question. Kindly post the other question seperately.…

Q: cos (In z) sin (In x) dx

A: To Evaluate the integral

Q: Find the tangent line to the function f(x) = 2x cos4(x) at the point (0,1)

A: We have given function fx=2xcos4x and point 0,1. We have to find tangent line to the function at the…

Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

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Q: Integrate: | cos" z dx

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Q: 3. Show that sinh a + sinh y = 2 sinh cosh %3D

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Q: ayfor gen f(x) = cos (2r + (/2)), a = /4 TT

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Q: If Z= sinh () show that: *=+y==0

A: GivenZ=sinhyx

Q: (27 (b) Show that 0. 4 tanh- 2x dx In 8. 16

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Q: (A) Prove that: cosh x + sinh x = e*

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Q: Use Simpson's rule with n = 6 to approximate cos(x) rp-

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

A: 1) The given equation is y=cosπ+sin-14x+xcosx+4x3 To find: dydx

Q: 33. Prove for a > 0: dx x2 + a 1 tan Ja

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Q: Find the derivative of y with respect to x, and 0 as appropriate: y = 6(sin (In 6) + cos (In 6) а.)

A: Given equation is: y=θsinlnθ+coslnθ Differentiate each term of y with respect to θ:…

Q: Prove that: sin z = sin x cosh y +j cos x sinh y

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

Q: IT Evaluate the integral: (cos x + sin x cosx)dx

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Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: Prove the identity. cosh(x) + sinh(x) - e

A: To prove the given identity we uses basic expression for sinh(x) and cosh(x).

Q: the integral of tan^2 (x) cos^3 (x)dx

A: To evaluate the given trigonometric integral

Q: sinx f(x) = on [0, 2n] cos x-V2

A: Given :         f(x) = sin xcos x - 2 on 0, 2π   To determine the extrema of the above function…

Q: 3. Use Simpson's rule to calculate x² sin x dx to within 2 × 10-5 of the exact value.

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Q: Evaluate integral 0 to pie sin 2 x cos 4 x dx

A: To Evaluate the integral given below:-I=∫0πsin2(x)cos4(x)dx

Q: is The third derivative of y = cos 3 1 sin 27 1 a) y" b) y" =- cos %3D %3D | - 3 27 3

A: The given differential equation is : y=cosx3   -1

Q: 1. If y= tanx, prove that y"=2(y² +1)(3y² +1).

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Q: Show that ∫∞−∞ sin x dx diverges.

A: To Show: ∫-∞∞sinxdx diverges.

Q: +15 - If y = cos-1(x) , Prove that dy -1 %3D dx /1-x²

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Q: Let f(x,y) = tan 1(sinh (y) + 2020 cos - 'y) + 4xy Calculate

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Q: Show that Sx cos*x dx = (x² + x sin 2x +cos 2x) + c

A: Given: ∫xcos2x dx=14x2+xsin2x+12cos2x+C.

Q: Use a linear approximation of f(x)=cos(x) at x=5π/4 to approximate cos(222∘)

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Q: 9. [sin Ssin' cos–dx 3 3

A: (9) To evaluate ∫sin5x3cosx3dx Substitute sinx3=u and cosx3dx=3du. Therefore,…

Q: Evaluate integral 0 to pie sin 2 x cos 3 x dx

A: Explanation: Given that,  ∫0πsin2xcos3xdx   Formula Used: Trig. identity:1-sin2x=cos2xSum rule of…

Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

A: