1. Find a formula for the inverse. f(x)% 3D 4x° - 5 (x)3D (X) D) (Simplify your answer. Type an exact answer, using radicals as needed.)

Q: 2 1) F(u) = sin 2au (sintu+cosu)

A: There are multiple question. As per company policy kindly ask other question separately.

Q: X° COS 4-x² dx -2

A: I=∫-22 x3cosx2+12  4-x2   dx     I=∫-22 x3 4-x2 cos x2+4-x22 dx →          1       Use property…

Q: 4x +1 = cos y?

A: According to guidelines we should have been able to solve only one question at a time

Q: Find the solution for the equation below. * + 6x + 10x = e-31 cos t

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Q: 4. Se2x sin(3x) dx

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Q: Evaluate dx 1²√√²-49) SV x>7, using a trigonometric substitution.

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Q: Find the general solution of the equation. xsin ydx+ xcos ydy +2 sin ydx =0

A: The solution are next step

Q: 2e cos 2t

A: Given,       2elncos2t

Q: If f(1)=3, f(1)=1, g(x)=cos x, and h(x)=[f(x)]/[g(x)], then what is h'(1)? Round to the nearest…

A: The given mathematical expression is the derivative, which can be determined with the help of…

Q: 10T cos e do =

A: We need to evaluate the definite integral. We know that integral of cosx is sinx. The solution of…

Q: The x2- 4 dx can only be evaluated using trigonometric substitution technique . A True B) False

A: To find if the given integral can be solved only by algebraic substitution technique.

Q: e) Σ sin(nx) ;x € [0, r] n3

A: We have to check whether the given series converges uniformly or not by Weirrstrass M-test. (e).…

Q: The x² – 4 dx can only be evaluated using trigonometric substitution technique . A) True B False

A:

Q: he displacement d​ (in meters) of an object at time t​ (in seconds) is given by the following…

A: The displacement of the object is d=2+3 cos 9π4t The above equation is in the form of simple…

Q: п What happens to x cos(nx)dx when n = 0? Justify your answer.

A: First of all, consider the given integral value and integrate.Let nx = a.Calculate dx and the limits…

Q: Q Is the equation e + x cos x 2 = 0 has real roots?. -

A: To show there are real roots, just use intermediate value theorem on appropriate interval.

Q: OBTAIN THE GENERAL SOLUTION 1. X cos? ydx = + tan ydy

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Q: Express e(3−5i)x in terms of trigonometric functions.

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Q: Eliminate all the arbitrary constants in the equation as follows: y = Ae2x – e-5x(B cos 2x + C sin…

A: The solution is given as

Q: (c) Show that e* sin(x²)dx < e – 1.

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Q: a. 2 cos 3x dx

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Q: Consider b. () 2: x dx e-2 sin 5 a

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Q: L x² cos 2x³ dx? After substitution is performed, which of the following is equivalent to

A: Given that the integrals  To find the evaluate and choose the correct answer

Q: (T/2 cos® x dx Determine the reduction formula for cos" x dx and then find

A: Given, ∫cosnx dx∫0π2cos6x The reduction for the above integral will be,   ∫cosnx dx=cosn-1x sin x…

Q: COS dx 1– 2 sin r

A:

Q: Consider solving x²V1-x² dx using trigonometric substitution. Which of the following is true? a. 2…

A: In trigonometric substitution method, the variable is substituted with a trigonometric function to…

Q: The S- 3 dx is 5 sin 6x

A:

Q: dx If x2 - 2x – 4 is solved by trigonometric substitution, which of the following substitutions is…

A:

Q: Suppose A is the annihilator of y= e*sin(x) – 3cosh(x), if f(x) = A(sin(x)), determine the value of…

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Q: 2 cos 0 d 1 - sin A

A: We can find the integration as below.

Q: (i) y= 3e –e**2 +2 sin (x² +1)

A:

Q: Eliminate all the arbitrary constants in the equation as follows: y = Ae2x – e-5x (B cos 2x + C sin…

A: To eliminate all the arbitraty constants in the below equation. y=Ae2x−e−5xBcos2x+Csin2x

Q: a) y = cos(e 2x) (e2x) -1

A: Differentiate wrt x

Q: dx If x2 – 2x – 4 is solved by trigonometric substitution, which of the following substitutions is…

A:

Q: Using appropriate substitution, ſ sin1º(x)cos³(x)dx is equal to: an

A: By using integration by substitution.

Q: Sec A - cos A is identically equal to

A:

Q: Eliminate all the arbitrary constants in the equation as follows: y = Ae2x – e -5x (B cos 2x + C sin…

A: Solve the above question.

Q: ez² cos(z) dz .

A: In this question, we use the Cauchy theorem for f(z).

Q: sin 3x (x² +16)² dx

A:

Q: b) L{e" sin(3t)}

A: b) We need to evaluate the Laplace transform of the following expression e2tsin3t

Q: Solve the following trigonometric equation for 0 ≤ x ≤ 2π. Explain your process.  cos 2 x −  1 = 0

A: For the solution of the problem follow the next step.

Q: If g (x) = sinx dx and =3, then g (0) is equal to A) 2 В -2 4 D

A: To find the solution.

Q: 2. Write the equation of the function in the form of y a sin b(x-c) +d,a> 0, and in the form y = a…

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Q: 4. How many solutions for x would the following equation have for any positive value of b? Justify…

A: Given:   for the given tan bx =12,…

Q: What is the frequency of the periodic function f(x) = 5 sin()?

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Q: 4. Find du for the equation 3y? – cosy = x° -

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Q: dx If x2 - 2x - 4 is solved by trigonometric substitution, which of the following substitutions is…

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Q: Find y'. а. уе* 3D х сos y b. In(3y) %3D 2х + Зу?

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Q: cos (x-Inx) dady. at.

A: Here, from the limit of integration, the integral is bounded by x=1e,x=1y,y=1,y=1. Plot the curve as…