6. Prove that 1 cosh(tanhx) : -1

Q: Express the limit as a definite integral on the giveninterval.

A:

Q: Determine whether the following impoper integral converges or diverges: (Hints: First use…

A:

Q: Evaluate the integral. 6. 6 cosh (x) dx X, 4

A: Let x=u Differentiating both sides with respect to 'x', we get ddxx=ddxu12x=dudxdxx=2du

Q: Evaluate the improper intergal 1 dx using the residue (x² + 100)? theorem.

A: The given problem is to evaluate the given improper integral using the residue theorem. We have to…

Q: Express the limit as a definite integral on the given interval. [9(x†)3 – 4xj]Ax, [2,9] lim n- 00 i…

A: Express the limit as a definite integral on the given interval.

Q: Conclude on the convergence or divergence of sin x dx cos x

A: Since function is not continous at x=pi/2. Hence we break the limit of integral at x=pi/2. This…

Q: 1. Approximate the value of each of the following definite integrals using: i. Trapezoidal Rule

A: As per Bartleby's answering policy, we can answer only one question, so kindly post the remaining…

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

A: Given integral, ∫tan3x dx

Q: Express the limit as a definite integral. n 7 lim 2 3x Ax: [2,7] Ax,0 k= 1 O A. 3x' dx 2 о в. 3x'd…

A: We have to express the given series as a definite integral.

Q: 12)Use the Trapezoidal Rule to estimate the integral ₁√x² - 1 dx using 4 intervals. Round to the…

A: Solve the following

Q: Find a value for n to ensure that the absolute error in approximating the integral x cos x dx by the…

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Q: Express the limit as a definite integral on the given interva lim [2(xf)³ – 5x¡]Ax, [2, 5] n- 00 i =…

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Q: Find the integral m tanx 1+x?

A:

Q: 23. Find the point c that satisfies the mean value theorem for integrals on the interval [1,4] for…

A: The given function is: f(X)=2x2-7x, [1,4]

Q: Use the addition formulas for sinh x and cosh x to prove tanh u + tanh v tanh(u + v) = 1+ tanh u…

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Q: Q1- Prove that coth x = 2 csch 2x + tanh x

A:

Q: Determine, with justification, whether the integral below converges or diverges. dx x15-|sin a|…

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Q: Q1- Prove that coth x = 2 csch 2x + tanh x %3D

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Q: Express the limit as a definite integral on the given interval. lim (2-5(x,)² + 6(x;")³] Ax, [0, 4]…

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Q: None Q2) prove that cosh(x + y) = coshx coshy + sinhx sinhy

A:

Q: calculate the integral.

A: Let,

Q: Express the limit as a definite integral on the given interval. -Дх, +7 [1, 6] lim dx J1

A: The following limit is expressed in the definite integral as shown below

Q: Evaluate the definite integral. ∫(lower bound=π/4)(upper bound=0)sin(4t)dt

A: Given,             ∫π40sin4tdt

Q: set up an integral ....bounds x=3pi/4 x=-pi/4 y=-sinx and y=-cosx

A: GRAPH

Q: Express the limit as a definite integral on the given interval. n *2 lim 2x;* + (x;") Ax, [1, 6] i =…

A:

Q: 3. Express the given integral as the limit of a Riemann sum but do not evaluate: So (x³ - 6x) dx.

A: Solution:-

Q: Express the limit as a definite integral on the given interval. x; In(1 + x3) Ax, [2, 3] lim 3 dx

A:

Q: Use Simpson's Rule with ne4 to estimate Cos"xdx COSTX ☺ For ☺ an upper bound for the estimate. Hint:…

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Q: Find the integral. 5sinh x -dx 1+cosh x

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Q: Express the limit as a definite integral on the given interval. lim n- 00 [4(x;)³ – 4x;"]ax, [(2, 7]…

A:

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

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Q: Evaluate the integral: S(sec(x) tan(x) + 4•x)dx .

A: The given integral,    ∫secx.tanx+4.xdx

Q: Q5. Apply the mean value theorem for integrals to evaluate e Lim -dx. 2 + CoS x

A:

Q: Express the limit as a definite integral on the given interval. cos(x;) Дх, [Зл, 4л] Xi lim i = 1 4л…

A: By definition of definite integral as limit of sums is

Q: Evaluate the integral   upper 4 lower 9 of the (root of x) dx

A: To evaluate the integral

Q: Evaluate the definite integral In 4 tanh x dx

A: To calculate the value of the definite integral involving hyperbolic functions

Q: Express the limit as a definite integral on the given interval. exi Ax 3 + x; lim [0, 4] dx

A: We need convert summation in to integral

Q: Find the indefinite integral ∫cosh √x / √x dx

A:

Q: Express the limit as a definite integral on the given interval. cos(x;) lim n-0 i = 1 Дх, [2л, 5л]…

A: Given limn→∞∑i=1ncos(xi)xi∆xi in the interval [2π,5π]We need to express the limit as a  definite…

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: Express the limit as a definite integral on the given interval. lim x; In(2 + x²') Ax, [0, 2] i = 1…

A: Given, limn→∞∑i=1nxi ln2+xi2∆x And interval 0, 2

Q: 1 Use the definition of the hyperbolic functions to prove the identity 1- - tanh? (2x) cosh (2x)

A:

Q: Evaluate the definite integral.

A:

Q: 5 Only one of these calculations is correct to evaluate the definite integral x² In(x) dx 1 Using…

A: First we have to find h and it's corresponding formula.

Q: Express the limit as a definite integral on the given interval. lim (4(x")3 – 3x;]Ax, [2, 6] n- 00 i…

A:

Q: Express the limit as a definite integral on the given interval. lim [9(x,")³ – 4x†]Ax, [2, 6] n- 00…

A:

Q: Prove that for all x € [1, 00), – sinh (- |cosh'(x)|) = V -1. %3D Ouest!

A: Proving of function  sinh(cos-1(x))

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…