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Q: Use Simpson's rule with 4 sub-intervals to find a rational approximation ton = L dx. 1+x2 a Give…

A: Solution:

Q: Series to Rind use lim 1- Cos 2X

A: Use series expansion of the e3x and cos 2x with help of ex and cos x:

Q: Show that cosh t + sinht = e and cosht - sinht = e. Hence, show that cosht- sinht=1. Deduce that…

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Q: 1. Write an expression for the evaluation of the integral sin x² dx by the trapezoid rule using n =…

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Q: 101 Jzy cosu(x) + sinh(x)

A: Given differential equation:d2ydx2-y=coshx+sinhxTo find: General solution. Note:1 coshx=ex+e-x22…

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Q: 53. Find the value of 1 dx using weddle’s rule. 1+x?

A: Weddle's law is a formula for solving numerical integration.

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A: We have to evaluate the integral ∫2532+x2dx by Simpson's rule-breaking it into 6 intervals.

Q: Find the lower sum for f(x) = sin(x) over the interval 0, 4, with n = 6. Submit your answer with…

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Q: Use differentials to approximate the value of √81.1 .

A: Use differentials to approximate the value of √81.1 .

Q: Which hyperbolic functions are increasing on their domains? A. tanh x and cosh x are increasing on…

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Q: Σ(²√5 - 1)" I=V 8 Do 1 n²-Ln Σ (Lan Ja (kan) n=2

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Q: 1. What is r^2?

A: a. x y xy x2 y2 925 750 693750 855625 562500 1600 1250 2000000 2560000 1562500 825 1050…

Q: Find the upper sum for f(x)=sin(x) over the interval [0,π/2] with n=6. Round your answer with three…

A: Given: The given function is fx=sinx. To determine: The upper sum of the given function over the…

Q: /8.9

A: Given : 8.93

Q: 10. It has been lo ponents produced in a certain factory are de hundred is drawn from each day's…

A: A random sample of size one hundred is drawn; n=100 1% of electronic components are defective;…

Q: Approximate using differential √627( answer in fractional form)

A: Let y=f(x)=x4where x=625 & ∆x=2

Q: he average speed / (t) (measured in kph) of traffic in a certain PM to 8 PM on a typical weekday is…

A: Given:

Q: Evaluate fx" In x dx for n ‡ −1. Which method should be used .-1 to evaluate fx-¹ In x dx?

A: We have ∫xnlnx dx   , n≠-1 Integration by parts is ∫fg dx=f∫g dx-∫ddxf∫gdx dx Using integration by…

Q: IATH 205 Calculus I Z #10 n+1 nt1 integral: sin(0)de

A: Given: ∫-ππsin θdθ

Q: 1 Proof (I): (sinhx)' = Vx? +1

A: Given: The equation is sinh-1x'=1x2+1. To prove: The main aim is to prove the equation. Concept: The…

Q: Show that O tanh(In x) = x² -1 O (cosh x + sinh x)" = cosh nx + sinh nx %3D

A: From the given problem:   tanhlnx=x2-1x2+1   As we know that :   sinhx=ex-e-x2 ; coshx=ex+e-x2   So,…

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

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Q: 2. A donkey is tethered to a corner of a field which is fenced in two directions. The rope is 10 m…

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Q: B. %23 Explain how you can prove that LA LC.

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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: Show that O tanh(In x) = (cosh x + sinh x)" = cosh nx +sinh nx

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Q: 22. Evaluate dr. x2 – 8x – 9 - a. cosh-1 -4 b. 4 cosh-1* – 4 +C C. sinh-1 – 4 5 +C d. 4 sinh-1 - 4…

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Q: Eind to approximation to Jas corect decimal an three places

A: The given expression is 253. Let y=x13, where x=27,∆x=-2 as 25=27-2. That is, y=2713=3 Obtain ∆y:…

Q: How do you approximate 1/4.998 using differentials? P

A: Linear approximation at a point :Let a function f(x) is differentiable at a point x=a , then the…

Q: 3 tanh (In(4x)) sech" (In(4x)), I) y = tanh (In(4.x)) [y

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Q: on inteaurron (ii) Determine the general formula for V Pn.

A: Numerical analysis.

Q: A pply Taylor's s expansion and find the se yies for tann at = 4 %3D

A: We need to find Taylor's expansion for tan2x at π4.

Q: Use differentials to approximate the value of (2.001)’.

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Q: etermine the length of y=ln(secx) between x=1 to x=π/4

A: Given: The curve is y=lnsecx since, x=1 to x=π4. Solution : The length formula L is given by formula…

Q: 1/4 f O √x sinx ²dx

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Q: evaluate using the appropriate method or combination of methods.

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Q: cosh(2x) = cosh?(x) + sinh² (x).

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Q: 2. Integrate the expression below using Trapezoidal Rule with interval width of 3.00 units. (sinh x…

A: In the question we have to solve the given integral by Trapezoidal rule with interval width of 3…

Q: on the interval 0sxs 2. Note: Water weighs 62.4 Ib/ft3. 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 -2 -1.5 -1…

A: Given y=15x2

Q: Find the average value of the funetion over the given inter s6) =8-x² on [-3, 12] a) -93 b) -31 O c)…

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Q: se hiemann sum with n=3 terms tod approximate the value ot 2. dx

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Q: Find the corresponding area using the attached z-table a) between z=0.25 and z=1.74 b) between…

A: a)P(0.25<Z<1.74)=?=P(Z<1.74)-P(Z<0.25)=0.9591-0.5987=0.3604   z-table :

Q: Compute F+1/F correct to eight decimal places for 1 ≤ n ≤ 10. Compare each value to the value of…

A: To compute: Fn+1Fn for 1≤n≤10. and also compare with the golden ratio.

Q: 1. cosh (j) 2. tanh 3. 3. In(2 + j3)

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Q: converges or div rge 2n+ Sinln)

A: The given series is  ∑n=1∞ 12n+sinn We have to check whether the series converges or diverges.

Q: Use Simpson's rule with n = 4 to approximate 5/ a2 + xdx Keep at least 2 decimal places accuracy in…

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Q: dx by taking four 1+x Use Simpson's Rule to obtain the approximate value of intervals.

A: Given: ∫0111+x2dx Definition: If f(x) is continuous on [a, b] then Where, ∆x=b-an