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- 3. True False. If false create functions that prove it is false. Note: f(x) = g(x). a) If_lim ƒ(x) = ∞ and_lim g(x) = ∞,then_lim [ƒ(x) − g(x)] = 0 x→ 0+ x→0+ x→0+ b) If h(x) and g(x) are continuous at x = c, and if h(c) > 0 and g(c) = 0, then h(x) lim. will = x→c g(x) c) If lim f(x) = 0 and lim g(x) = 0 then lim f(x) does not exist. x-a x-a x→a g(x)arrow_forwardPls help ASAParrow_forward15. a) Consider f(x) = x-1 3x+2 and use the difference quotient to determine the simplified expression in terms of x, for the slope of any tangent to y = f(x). Also, determine the slope at x = 2. 15 b) Determine the equation of the tangent to f(x) at x = 2. Final answer in Standard Form Ax + By + C = 0, A ≥ 0, with no fractions or decimals.arrow_forward
- Determine whether the series is convergent or divergent. Justify your answer. If the series is convergent, you do not have to find its sum. n=0 (-1) 72n+1 (2n)!arrow_forwardQ5: 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.arrow_forwardQuestions 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.arrow_forward
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