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A:
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A:
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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
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A: Topic = Derivative
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A: The theoretical error bound in approximating the integral∫0πsinx2dx using Boole's rule is shown…
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A: We will prove the inequality as following.
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A: Fundamental inverse Trigonometric Identities: →cosh2y - sinh2y = 1 Basic derivative:…
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A: To Evaluate the integral
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A: arccos1-2x2 Put x=sinθ, we get arccos1-2x2=arccos1-2sin2θ=arccoscos2θ ∵cos2x=1-2sin2x=2θ=2…
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A: A detailed solution is given below.
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A: Explanation is given below...
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A: Prove that: sinh 2x = 2 sinh x cosh x
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A:
Q: a 5. Using integration by parts twice, prove that the L (sin ax) %3D s2+ a=
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Q: (A) Prove that: cosh x + sinh x = e*
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A: Let's find.
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A: Given that sec2?tan2?d?To find : Integral Solution :∫sec2?tan2?d?Let, tan?=tsec2?d?=dt∫t2dtt33+c
Q: sin x + 10(csc x)² dx
A: To compute: ∫(sin x+10(csc x)2)dx
Q: prove that cosh(x + y) = coshx coshy + sinhx sinhy %3D
A:
Q: What is the integrable form of sin-cos-sino de? 2 (A -2 | sinu du B / Ju?- 1 du 2 /1-u² du D cosu du
A: Given: ∫sin θ2 cos θ2sin θ dθ Find the integral form of the given function. By using trigonometric…
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Q: Prove that: sinhx + coshx = e* %3D
A: we have sinh(x)=ex-e-x2cosh(x)=ex+e-x2
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A: To integrate: ∫-π2π21+cosxdx Solution: Property of definite integral states that: ∫-aafxdx=2∫0afxif…
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A: 1-1cosh22xUse the Hyperbolic identity: 1coshx=sechx=1-sech22xUse the Hyperbolic identity:…
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Q: IT Evaluate the integral: (cos x + sin x cosx)dx
A:
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: 5) Use the Fundamental Theorem of Calculus to define of the function fol=sin (x?+!) ant-derivative…
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A: Consider the given L.H.S of the given identity coshx+sinhhxn
Q: prove that cosh(x + y) = coshx coshy + sinhx sinhy
A:
Q: What is the integrable form of sin-cos-sine de? 2 2 V1-u? du -2 sinu du u² – 1 du 2/ cosu du
A: We have given integral Let, I=∫sinθ2cosθ2sinθdθ As, sin2x=2sinxcosx sinx=2sinx2cosx2 So,…
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A:
Q: (b) Prove that : - 1) (coshx)2 - (sinhx)2 = 1 ,2) coshx - sinhx = e, 3) (cothx)2 -1= (cschx)2 %3D
A: Use hyperbolic function
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A: Y1=cos5t and y2=sin5t do not a fundamental set of solutions of differential equations y"+16y=0
Q: B) Prove that: cosh (x + y) = coshx coshy + sinhx sinhy %3D
A: We know that cosh(θ) = eθ+e-θ2sinh(θ) = eθ-e-θ2
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Q: d. tion to prove that (cscx) dx = – CSC X COt x. 86. Use the quotient rule and the derivatives of…
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Q: limit x approaches zero, sin^2x/x
A: Given,
Let .
Then .
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