Consider the following function. 9 cos(TX) f(x) = 9 cos(an) What conclusions can be made about the series and the Integral Test? O The Integral Test can be used to determine whether the series is convergent since the function is positive and decreasing on [1, o). O The Integral Test can be used to determine whether the series is convergent since the function is not positive and not decreasing on [1, c0). O The Integral Test can be used to determine whether the series is convergent since it does not matter if the function is positive or decreasing on [1, c0). O The Integral Test cannot be used to determine whether the series is convergent since the function is not positive and not decreasing on [1, c0). O Thore ic not onough information to dotormino whothe Integral Tost can bo used or ne

Find the dimensions of a rectangle with perimeter 100 m whose area is as large as possible. m (smaller value) m (larger value)

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QI: If the vectors a and b are perpendicular, find the value of 2. d = 3i + 4j – 2k 5 = -2i + 3j + Ak

4x - 10 Let f(x)=1-(2x-5)4¹ a. Find the Taylor series representation for f about x = 2.5 that is valid for all x € (2,3). Hint: Use the equation t", where t € (-1,1), to find the Taylor series representation for x=0 1 about x = 2.5. Then, use this series to find the desired series representation for f. 1-(2x-5)* b. Use the result in item 2(a) to find the 5th degree Taylor polynomial of f about 2.5. c. Use the result in item 2(b) to approximate f(2.55). Express your answer in decimal form. +00

Evaluate the infinite series by identifying it as the value of an integral of a geometric series. (– 1)" 87 +1(n + 1) 2 In (3) x n=0 1 n+1 |f(t)dt se)dt where f(=) = (- )"(;) 1 x" = Hint: Write it as 8 8 + x n=0

Solve both part