Chapter 10.3, Problem 49E

Q5: 06: the foot lies between 3 and 4. (20 Marks) Let f(x) = 3*, use Lagrange interpolation to find a second-degree polynomial that agrees with this function at the points x₁ = 0, x₁ = 1, x2 = 2.

Questions An insurance company's cumulative incurred claims for the last 5 accident years are given in the following table: Development Year Accident Year 0 2018 1 2 3 4 245 267 274 289 292 2019 255 276 288 294 2020 265 283 292 2021 263 278 2022 271 It can be assumed that claims are fully run off after 4 years. The premiums received for each year are: Accident Year Premium 2018 306 2019 312 2020 318 2021 326 2022 330 You do not need to make any allowance for inflation. 1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method. (b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method. 2. Comment on the differences in the reserves produced by the methods in Part 1.

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Using f(x) = log x, what is the x-intercept of g(x) = log (x + 4)? Explain your reasoning. Please type out answer

The function f(x) = log x is transformed to produce g(x) = log (x) – 3. Identify the type of transformation and describe the change. Please type out answer

Each graph below is the graph of a system of three linear equations in three unknowns of the form Ax = b. Determine whether each system has a solution and, if it does, the number of free variables. A. O free variables ✓ B. no solution C. no solution D. no solution E. 1 free variable F. 1 free variable

+ Find the first five non-zero terms of the Taylor series for f(x) = sin(2x) centered at 4π. + + + ...