Prove the identity. cosh(x) + sinh(x) = e* cosh(x) + sinh(x)

Q: 9. cosh x + sinh x= e* %3D

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Q: 9. cosh x + sinh x = e* %3D

A: To Prove,                cosh x+sinh x=ex

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: Solve indefinite integral ∫ cos(πx)/sin^3(πx) dx

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Q: X sinx cosx dx

A: To Determine: find the integration  Given: we have ∫x cosx sinx dx Explanation: we have ∫x cosx sinx…

Q: cos x ln(x - *) *-+ In (e-e*) 6. lim

A: Topic:- limits calculus

Q: lim x→0 (sin10(x)cos(8x))/x=?

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Q: dx sinh x - cosh x

A: To Evaluate: ∫dxsinhx-coshx Concept: i. ∫afxdx=a∫fxdxii. ∫exdx=ex+C

Q: Solving it with gamma and beta function 1 dx - Ln x

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Q: sin 2n x Prove that: dx = 0 for all n e N. sin x

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Q: Using e and e expansions, find sinh x.

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

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Q: =) S sin6 x+cos6 x sin³ x cos³ x dx

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Q: 15. sinh 2x = 2 sinh x cosh x %3D

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Q: Evaluate the limit.

A: Given that, limh→0sin(2h)(1-cos h)h2 Because of the direct substitution of h = 0 into this, we get…

Q: eiz-e-iz 1. Show that Sin z 2i

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Q: sinh x + cosh x)ª= e4x

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Q: II. Perform the integration. sinh (e-") dx e² cosh(e-¤) 4.

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Q: (2) Compute the value |* sin(2r)dr and show the computations involved. If you are using substitu-…

A: We use integration by parts.

Q: Find the indefinite integral. ∫(x2 cos x)dx

A: The given integral is ∫x2cosx  dx. Let u=x2  and   dv=cosx dx. This implies that du=2xdx  and…

Q: Review of Definite & Indefinite Integrals 1 dx is -da The value of

A: In definite integral we take upper limit and lower limit but indefinite represents family of…

Q: 75. Evaluate / sin x In(sin x) dx. Hint: Use Integration by Parts as a first step.

A: Let,

Q: c Functions. Prove the identity cosh x – sinh x = e x-

A: We have to show the given condition

Q: Q-6: Evaluate the integral 1). dx So Jie-1

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Q: sin-'(-i) = %3D -i log(i + /2) o -i log(1 – /2) i log(1 + /2) -i log(1+ /2)

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Q: Prove the pollowing identity.. (sin x t cos L cas x)- sin 2X-CoS T Sin'x + Cosx

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Q: sin? 6, determine a reduction formula for the 5 By the substitution x = integral 2(1- x)2 dx. Hence…

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Q: 14. ſ e sin40 cos40d0

A: (14). To integrate: ∫esin4θcos4θdθ Substitute  t=sin4θ t=sin4θdtdθ=4cos4θdt4=cos4θdθ Substituting…

Q: 2 – sin x |log -п/2 .피2 dx 2 + sin x.

A: Given: I=∫-π2π2log2-sinx2+sinx-exdx For evaluating given integral, we use property mentioned below…

Q: cos*(x)dx

A: According to integration reduction formula ∫cosn(x) dx=n-1n∫cosn-2(x) dx+cosn-1(x) sin (x)n . For…

Q: integral e -x cos 2x dx

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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: Example Let sinh(2)e f(2) Find the residue at z = 0.

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Q: et +e» et Рe-* cosh(x) sinh(x) 2

A: Given that:- coshx=ex+e-x2 sinh(x)=ex-e-x2

Q: cosh(2x) = cosh?(x) + sinh² (x).

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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: lim E(cos (27x;))Ar over [0,5] COS i=1

A: The definite integral is defined as  ∫abf(x)dx=limn→∞∑i=1nfxi*ΔxWhere, Δx=b-an, xi*=a+iΔx The…

Q: sinh- x = In 2.

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Q: e2x+Inx² sin x² dx -+fe²x cos x² dx

A: This is a problem related to integration. Based on the general formula we will solve the problem.

Q: cos x F(x) = sin-1 1+sin x. F(x) = In ln In x

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Q: ∫ln a/x sin^-1x dx

A: Given,           I=∫ln(ax).sin-1(x) dx To solve this integration we apply integration by parts…

Q: 1 lim, (e** - 1)sin-+9cos x . x0

A: Given: limx→0ex2-1sin1x+9cosx we know that  limx→0ex2-1=0 and  limx→0sin1x=-1 to 1 so,…

Q: Find Sn{sinh(x)} = %3D O A. Lnn(-1)" sinh(L) L2+n2n2 O B. None O C. Lnt(1-(-1)" cosh(L)) L² +n²n² O…

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Q: Verify the identity sinh(x + y) = sinh x cosh y + cosh x sinh y

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Q: sinh (e-*) dx e* cosh(e¯*)

A: Given,∫sinhe-xexcoshe-xdx

Q: Prove the identity.  cosh x - sinh x = e -x

A: Consider the given identity of L.H.S as coshx-sinhx

Q: Prove the identity.   sinh(x+y) = sinh x cosh y + cosh x sinh y

A: To show that sinhx+y=sinhx coshy+coshx sinhy

Q: Expand Sinx by Maclaurin's Theorem. Expand log(a+h) by Taylor's Theorem.

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Q: 11. Find the positive root of x - 2 sinh x +1 = 0.

A: We have to find the positive root of x²-2sinhx+1=0 The formula for finding the root of equation by…