Exercise 2: Use Taylor's theorem to estimate cos(2/3) to within 0.001. Make sure to prove your estimate is correct Exercise 3: Use Taylor's theorem to estimate V126 to within 0.00001. Make sure to prove your estimate is correct Exercise 4: Use Taylor's theorem to estimate V2 to within 0.00001. Make sure to prove your estimate is correct.

Q: Find the smallest integer n to guarantee that the error in using Tn to approximate | e dx is e less…

A: The integral is ∫01ex2dx  The error of Tn is obtained by the formula is E=-b-a212n2f''c We want…

Q: Find the total differential. z = e-X tan(y)

A: Given, fx=z=e-xtany To find fx=z

Q: Calculate the energy coefficient from the first order if the infinite potential box is as uneasy as…

A: Given: φn=2LsinnπxLφ2=2∂Lsin2πx2L To find: Solution

Q: Find the equation of the tangent line to the graph of f(x) = 9 sin(x) + 4 cos(x) at x = in in the…

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Q: Find General Solution on this Diffential E Qution by using (uC set) =e +Sin X

A: Given differential equation is y''+y'-2y=ex+sinxfind the general solution

Q: / Use the Newton - Raphson method to estimate the root of f(x) = e* - x , employing an initial guess…

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Q: Use Newton's Method to find an approximation of V5+1 accurate to within 10-3

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Q: b. Find the value of V1- 0.162sin²x dx using Simpson's 1/3rd rule, taking 6 equal subintervals

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Q: Find a root of the equation 3x + sin(x) - e* = 0 using Newton Raphson Method. Consider initial guess…

A: Let fx=3x+sinx-ex Then f'x= 3+cosx-ex Given that x0=2·500

Q: Compute for a real root of 2 cos x – sin vx = i accurate to 4 significant figures using Fixed-Point…

A: 2cosx3-sinx=14  compute for a real root of equation using fixed point iteration method with an…

Q: (b) Evaluate 1 dx using Romberg's S. 1 + x2 hence obtain an approximate value of T.

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Q: A stone, projected vertically upward with initial velocity 112ft/sec, moves according to…

A: Topic = Algebra The maximum height reached by the stone is 196 ft.

Q: (a) Consider the task of approximating e-4=* dx using the Composite Trapezoidal rule. How large…

A: As per bartleby guidelines we only give first question answers.

Q: part C

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Q: P (a, b) = So -at² _e-bt2 dt %3D t2

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Q: Find a suitable method for integration of Sin (x²) x = 0,√ using a two-point sample of Sin (x²) x =…

A: We have to find the integration I=∫0πsinx2dx let f(x)=sinx2 For ∫abf(x)dx, two point formula is…

Q: Hello! Can you help me with this calculus problem? I think I got something very wrong.

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Q: The approximation of x' e¯*dx by Simpson's Rule is O 0.162402 O 0.160603 O 0.160602 O None of these…

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Q: Compute for a real root of 2 cos T – sin T = accurate to rignificant figures using Fixed-Point…

A: The following steps are used to find the numerical solution of the equation fx=0 by the fixed point…

Q: Prove that E = ehd.

A: By the defination, fx=fx+h....1∆fx=fx+h-fx∆fx=Efx-fx∆fx=E-1fx Therefore, ∆=E-1E=1+∆.....2

Q: Find the temperature u(x, t) in a rod of length L, if the initial temperature is f (x) = 100 sin 6nx…

A: Given function is, fx=100sin6πx at x=0 and x=L Now, we know that, ∂2t∂x2+qgk=1α·∂t∂z....(1)

Q: Use differentials to approximate v410, and then compare your approximation with the actual answer…

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Q: 300r Integrate numerically: f (x) = 1+e from 0 to 10 using 5-segment trapezoidal rule. Round-off the…

A: Solution

Q: Find the average velocity during each time period. s = s(t) = 3 sin(tt)+ 2 cos(Tt). (i) On the…

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Q: Compute an approximation to the value of Le-x*dx a) using Simpson's Rule b) using Simpson's…

A: The composite Simpson's rule approach is a frequent way to deal with issue. To accomplish this,…

Q: A stone, projected vertically upward with initial velocity 112ft/sec, moves according to s = 112t −…

A:

Q: Q1:Choose theappropriate value to integrate the following sin(In x) dx (sin (In x) – scos (In x)) +…

A: Solution I=∫sinin x dx        Let  lnx=t⇒x=et         1x dx=dt          dx=xdt…

Q: Find the linear approximation of f (x) = ln e at L() In(1.42) 1 and use it to estimate ln(1.42)…

A: Given function is f(x) = ln x and the linear approximation is to be calculated at x = 1.Linear…

Q: . Compute for a real root of 2 cos VI – sin Va = + accurate to 4 significant figures using…

A: Given equation is 2cos x3 - sinx =14 And, initial guess:- x0 =π Also, 2cos x3 - sinx =14⇒ x  = cos-1…

Q: Use Gaussian Quadrature of order 5 to approximate 08 6 2 x-1 To how many decimal places is this…

A: Given that,    f(x)=∫286x-1dx                                  1 Using the Numerical Integral by…

Q: Verify the given linear approximation at a=0 . Thendetermine the values of  x for which the linear…

A: Concept Used: Linear approximation of f(x) at x = a is

Q: Find the temperature u(x, t) in a rod of length L, if the initial temperature is f(x) = 100 sin 6Tx…

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Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to %3D estimate I = [ S" In(2 +3/ã)…

A: Given that, the integral is ∫26ln2+3x1+x2dx and step length is h=0.4=25. From the given integral,…

Q: 2. Compute for a real root of 2 cos a – sin Va = + accurate to 4 significant figures using…

A: In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.…

Q: 4. Compute dx S in two ways and verify that the answers agree.

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Q: Use Newton's method to solve for x with an initial estimate of x0 = 2n with d* < 0.001. Cosxcoshx =1…

A: (cos(x))(cosh(x))=1f(x)=(cos(x))(cosh(x))-1ddx((cos(x))(cosh(x))-1)=-sin(x)cosh(x)+cos(x)sinh(x)⇒f'(…

Q: Use Taylor's formula with a = 0 and n = 3 to find the standard cubic approximation of f(x) = y at x…

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Q: The value of n when integrating the following function using Simpson's method is: [2²/ dx h = 0.2 >

A: solution is given below

Q: Create a second order DE (no need for IC's) whose sdution conuergio to O ao t+ o, without…

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Q: Find the soluon of following ordinary dtifferential equatTon

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Q: Use Newton's Method to find an approximation to V25 correct to within 10-6 (use an appropriate…

A: Solution

Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+37) -dx, 1+x?

A: According to the fundamental theorem of calculus ∫x0xnf(x)dx=F(xn)-F(x0), where dFdx=f(x). The…

Q: b. Find the value of V1-0.162sin²x dx using Simpson's 1/3rd rule, taking 6 equal subintervals

A: We apply Simpson 1/3rd rule it is given that six sub intervals must be mentioned so in the interval…

Q: se N.P.M. to estimate the root of -X = e -X for an initial of Xo =0

A: Here f(x)=e-x-x,  x0=0. We estimate the root of f(x)=0 by using N.R.M.

Q: An RL circuit has an emf of 5 V, a resistance of 50 Q, an inductance of 1 H, and no initial current.…

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Q: Compute for a real root of 1 2 cos Vx – sin vx = accurate to 4 | 4 significant figures using…

A: 2cos(33)-sinx=14;   x0=π f(x)=2cos(33)-sinx-14 f(x)=0 ⇒2cos(33)-sinx-14=0 x=cos-11214+sinx3=ϕ(x);…

Q: Use the Romberg integration to evaluate. 3 xe*dr With an exactitude e =0.5%

A: Given ∫03xexdx whose step error should be εs=0.5%. We use the Trapezoidal rule…

Q: -4 I cosx (0.25x² + 1.90)dx,use n =3

A: Given:        ∫14cosx0.25x2+1.90dx , n=3 The formula for the Trapezoidal rule:…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.