use the Mean value Theorem to establish Isine-siny 2-y) Ve,yER

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

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Q: Find an upper bound on the error that can result if cos(æ) is approximated by 1– (x/2!) + (x*/4!)…

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Q: Find the mean value of sin2x over the inteval (0,x)

A: Please see the whole answer first before confusing.

Q: Use the definitions of cosh x and sinh x to show that cosh2 x - sinh2 x = 1.

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Q: 10 Use aepropriate substitution Ond then a trigonometric oubtitution to evaleiate the integial. dx…

A: This question can be solved using the concept of integration by substitution.

Q: Show that the functions have exactly one zero inthe given interval. r(θ) = θ + sin2 (θ/3) - 8, (-∞,…

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Q: Find the mean value of sin2x over the interval (0,pie)

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Q: Find the absolute extremum point(s) of f(x) = e' -Cos x on [-골, T), E any.

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Q: Find the mean value of sin 2x over the interval (0,x)

A: Solution is given below:

Q: differentiate the funtion y = cosh x - sinh x / cosh x + sinh x

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Q: Find the mean value of over the interval [0,27] 4+ cosx

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Q: nd the mean value of sin 2x over the in

A: Here we have to find the mean value of sin 2x over the interval (0,x)

Q: 3x² dx

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Q: How does Taylor’s formula for a function ƒ(x, y) generate polyno-mial approximations and error…

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Q: Evaluate the definite integral. 2 cot-¹(x) 1+x² 1 - 1 -dx

A: To evaluate the integral.

Q: 4. Show that sinx can be approximated by x-x³/6 within 0.01 on the interval [-1,1].

A: see my solution

Q: Prove the identity sinh 2x = 2 sinh x cosh x

A: Prove that: sinh 2x = 2 sinh x cosh x

Q: ) Use Taylor's formula to estimate the error in the approximation In(x) ~ P3(x) or all x in the…

A: Since you have posted multiple questions but according to guidelines we will solve the first…

Q: (b) Use the definition to show that cosh(-x) = cosh(x). + e-(-x) cosh(-x) e-X + eX

A: Please refer the attached image for complete solution. THANK YOU.

Q: */16 etan(1r) sec2(4x) dr

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Q: Use a tangent line approximation to estimate the value of V3.9 O 2 O 1.998 O 1.975 O 1.95

A: Known fact: The tangent line approximation formula is fx+∆x≈fx+f'x ∆x. Given that 3.9. Consider the…

Q: State the Mean Value Theorem. Use it to show that for all x ≥ 0, 0 ≤ tan^−1 x ≤ x. [Hint: Use Dx…

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Q: 9) If f(x) = sinh() , then f'(x) = %3D (A) 3 cosh(÷)

A: Given: f(x)=sinh1x2To find:f'(x)

Q: Evaluate the definite integral using the Newton-Cotes quadrature formula (Simpson's Rule)

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Q: Use Secant method to find the root ofthe function:f(x) = 3x + sin x- e to 5 decimal places. Work…

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Q: (2x³ + 5x-4) dx

A: Solved below.

Q: Use the addition formulas to provesinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

A: Our Aim is to prove the following identities:-(a) sin h(2x)=2 cosh (x) sinh (x)Proof⇒Since, sinh…

Q: Use Newton's method to find the second and third approximation of a root of 3sin(x)=x starting with…

A: Here 3sin(x)=x∴3sin(x)-x=0Let f(x)=3sin(x)-x ∴f′(x)=3cos(x)-1 x1=2 1st iteration…

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

A: Given,             ∫π40sin4tdt

Q: prove that cosh(x + y) = coshx coshy + sinhx sinhy %3D

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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: Prove the addition formula for cosh x given by cosh(x + y) = cosh x cosh y + sinh x sinh y.

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Q: Estimate the error if P3(x) =x- is used to estimate the value of sin x at x= 0.4.

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Q: Evaluate the integral + tan sec dt

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Q: Use Secant method with p, =1, p, =1.2 to find the root of f(x)= In x-cos x that is accurate to…

A: Consider the given function  f(x)=lnx-cosx with initial estimate  po=1  ,        p1=1.2

Q: Prove that: sinhx + coshx = e* %3D

A: we have  sinh(x)=ex-e-x2cosh(x)=ex+e-x2

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1 Differentiate f at x = 0.5 using 5 point formula. Also…

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Q: Find all points on the graph of the function f(x) = 2 sin(x) + sin2(x) at which the tangent line is…

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Q: Prove that cosh(x±y) = cosh x cosh y± sinh x sinh y.

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Q: Hiwiy Express the ballowsing functions by Palar equationft 2.

A: To change a rectangular equation to a polar equation just replace x with (r cos θ ) and y with  (r…

Q: prove that cosh(x + y) = coshx coshy + sinhx sinhy

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Q: Find all points on the graph of the function f(x) = 2 sin(x) + sin2(x) at which the tangent line is…

A: Tangent line

Q: 2 = sin5t constitute a fundamenta L

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

Q: 8. Use Simpson's rule, with n = 8, to approximate fe sint dt. Compute the error if the true value

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Q: Determine the equation of the normal line to the graph of f (x) = (2 + sin 2x)²+sin¯(x*) at the…

A: Given; f(x)=(2 + sin 2x)(2+sin^(-1)(x^2)).

Q: The approximation of 1 = f*cos(x³ - dx using composite Simpson's rule with n= 3 is:

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Q: The diffakential equotion af Sc sinx after eleminating of the ar bitrary constant eis

A: The order of the differential equation is equal to the number of arbitrary constants. the given…

Q: limit x approaches zero, sin^2x/x

A: Given,

Q: DEvaluate VFano do

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…