(a) FAEN102 students must attend t hours, where t ∈ [0, H], of lecturesand pass two quizzes to be in good standing for the end of semester examination.The number of students who attended between t1 and t2 hours of lectures is de-scribed by the integralZ t2t120t2dt, 0 ≤ t1 < t2 ≤ H.As a result of COVID-19, some students attended less than H2hours of lecturesbefore the university was closed down and passed the quizzes so they are qualifiedto take the examination. Find the ratio of students who attended less than H2hoursof lectures(b) The final score each student got is proportional to the amount oflectures he/she had attended which is given by the functionL(t) = 100Ht.What was the average score in the class?

Q: (a) Find the quadratic approximation P2 for f (x) = In x at x = 2 (b) Use above to approximate…

A:

Q: Calculate the Taylor polynomials T3(x) and T3(x) centered at æ = T for f(x) = tan(x). T2(x) = T3(x)

A:

Q: there

A:

Q: The domain of the funsfon f(x) te 9) E2,21, or equivalenfly,t243 C) [4,00, 0r )(00,4),or…

A: This question can be solved by applying the concept of existence of function at various points on…

Q: Find the third Tayler polynomial P, (x) f fxl= cos X at

A: Given function is  fx=cosxat x=π

Q: 3. Use Müller's Method to determine all the roots of f(x) = x' -x² - x– 2 Choose x2=1.0, Xo=x2+dx2,…

A: Given:- fx=x3-x2-x-2 x2=1.0,x1=x2-δx2  ,x0=x2+δx2,  δ=0.01

Q: Q2= A) for E= 2xĭ-3Y3+K %3D prove That divc curl È)=0 %3D

A:

Q: - Find the antiderivative, FCx), and Check your answer of the funetionçiven xZ+3x+5 by f (x)=

A:

Q: t2 and y2 3 are two distinct solutions of the IVP t²y" – 4ty + 6y = 0, The functions yi %3D y(0) =…

A:

Q: (i) Construct the minimax polynomial p2 E P2 on the interval (-1,1] for the function g defined by…

A: As per the question we have to find the bset fit polynomial in p2 ∈ P , to to the curve g(x)=sin(x)…

Q: Consider the function f(x) = x³ + 2x + 5. 1. Estimate the root to two significant digits using…

A:

Q: 2. Expand the function f(x) = tan-1 x up to the first two non-zero terms in the Taylor's polyno-…

A: Solution is given below:

Q: 1. Consider y=f(x)%3Dsin(3x)+x² over [0, 37/2]. (By hand but use a calculator) a) Use the three…

A:

Q: 2. Estimate the root of f(x) = In x; ɛEs = 0.1%. Start the computation with values of xl = xi-1 =…

A:

Q: 2) Let f(T) e Q[T] be an irreducible polynomial of degree n > 1. Show that f(T) has n different…

A: We will use the basic knowledge of ring theory to answer this question properly, in detail.

Q: Q4) Find the root of f(x)= (x^2)-5, in interval [0,4] by using bisection method.

A:

Q: Let f(x) = , defined on [0, +). Find the 10th Taylor (b) polynomial T1o(x) centered at a = 2. 3+x

A: Taylor series is nothing but expressing the infinitely differentiable function in terms of its…

Q: 20. Let yapp (x) be a polynomial approximation, involving only one coordinate function, for the I(4)…

A:

Q: Q5) Evaluate the integral 0.61-10 (6.73x + 4.3025 - 10- dx 2.316 • 10-11 122-10- Using trapezoidal…

A: The solution to the integral can be calculated using numerical methods. The formula for the…

Q: : Use Bisection method to solve f(x) = 668.06 -0.146843X (1 - e )- 40 with Xu = 16 %3D and X1 = 12…

A: The function is fx=668.06x1-e-0.146843x-40 with the bounds xu=16 and xl=12. The error is less than…

Q: IB) Find the cnber of curvatee, eguation of the curde of cuuunfure f (x)> Jax of the gmph. of at x=…

A: Consider the given curve as, fx=2x at, x=4 Let y=fx=2x

Q: a) Let f(x) = 3x² + 2x – 3x-1 +72". Compute the integral of f. = x-1 and let h(x) = x² + 2x. Compute…

A:

Q: Find solution of an equation X f(x) 1.0000 1 1.25 0.8000 1.50 0.6667 1.75 0.5714 2.0 0.5000 a. Using…

A:

Q: The Taylor polynomial of order 1 generated by f(x)= cos-(x) at a == is Select one: a. 2 P¿(x) = 3 V3…

A:

Q: Consider f(x) e on [0, b] and its approximation by an inter- polating polynomial p2(x) at the evenly…

A: Given that f(x)=ex on [0,b]We have to approximate the above function in [0,b]i.e…

Q: V5 + v6 Find a monic integral polynomial for which x is a root and prove that x is algebraically…

A: We have x = 5+6. The objective here is to show that x is an algebraically irrational number.  An…

Q: (a) find the least squares approximation g(x) = a0 + a1x of the function f, and (b) use a graphing…

A:

Q: For the cubic polynomial function ?(?)=??3+??2+??+?,f(x)=ax3+bx2+cx+d, find ?,a, ?,b, ?,c, and ?d so…

A:

Q: what is the third-order Taylor polynomial approximation of f(x) = cos(x) around x. = h2/4-1 A h/2-1…

A: G

Q: (b) For f(z) find the residue of f (z) at the singular point (z+1)2(z2+4) z = -1

A:

Q: 2) Let f(x) = lIn(2x) Find 3rd Taylor Polynomial centered at c= 1 for f(x)

A:

Q: Use Taylor's Theorem to find an interval [ — z, z] where the Maclaurin polynomial p2(x) - = 1 1…

A: The given function is fx=cosx and Maclaurin polynomial p2x=1-x22. The Taylor's Theorem states:  If…

Q: Find the positive integer A such that t²x" +tx' + t²x = λx has a nontrivial solution satisfying x(0)…

A: Hint: Substitute t=ey , t2x''=D(D-1), tx'=D-1in the given equation and calculate to obtain the…

Q: Consider the function f(x) = x³ + 2x + 5. 1. Estimate the root to two significant digits using…

A:

Q: - Let Q(x) be a polynomial of degree less than N. Prove that Q(x)PN(x)dx = 0.

A: Note, that this result is a specific case of orthogonality of Legendre’ s polynomials. We will prove…

Q: 3.2 Let f(x) = Approximate the integral x4 x L f(x) dx using the Trapezoidal rule with n = 4. -2

A:

Q: Q5) Evaluate the integral 0.61-10 (6.73x + 4.3025 107 dx 2.316 10-11 1.22-10 Using trapezoidal and…

A: The integration can be calculated using the numerical method. The formula for the trapezoidal rule…

Q: (11) Let G(x) = 1 In(1+t²)dt. (a) Find G(1).

A: Solution Given G(x)=∫1xπ ln(1+t2)dt.We need to find the G(1)

Q: hat is the 5th Order Taylor Polynomial for f(x) = V1 + x where x = 0?

A:

Q: -Find the least squares approxtmation polynomial of degree two for the continuous function f(x), (x)…

A: Least square method to approximate polynomial: Least square method to approximate the two degree…

Q: 2. Verify that the Legendre Polynomials Po, P1, P2, and P3 satisfy Legendre's equation (1 ~ x²) dy…

A: Given Legendre's equation is (1-x2)d2ydx2-2xdydx+n(n+1)y=0                       (1) its Legendre's…

Q: Consider the function f(x) = x³ + 2x + 5. 1. Estimate the root to two significant digits using…

A: Given, fx=x3+2x+5 We have to find the root of fx in the interval -1.4, -1. In bisection method, if…

Q: Show that the Maclaurin polynomials for f (x) = sin x are x2n+1 T2n+1 (x) = T2n+2 (x) = x – 3!…

A: we have to show that  Maclaurin polynomials for    f(x)=sinx  are…

Q: Find the instantaneoui rale of change of the funclion at the specieled value of X, f(X)=X2-3; X= - 2

A:

Q: Compare the graphs of y = Vx, y = Vx, y = x, y = x², and y = x' on the interval 0 < x s 2. Write a…

A: Differentiate the expression of the slope with respect to x. For any value of x in the interval…

Q: Q2 : Use Bisection method to solve F(x) = 668.06 -0.146843% (1- e )- 40 %3D with Xu= 16 and x2 = 12…

A: We have to use Bisection Method to find approximate root of given equation

Q: Show that if an integration formula of the type I„(f) =£w;f(x;) j=1 is exact for 1, x, x², ...x",…

A: According to question given:Inf≈∑j=1nwjf(xj)Is exact for 1, x, x2, ...xm for a natural number m.We…