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For the following exercises, indicate whether each of the following statements is true or false. If the statement is false, provide an example in which it is false.
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- For the following exercises, use the graphs to determine the intervals on which the functions are increasing, decreasing, or constant. 30. Find the local minimum of the function graphed in Exercise 27.arrow_forwardFred has a piggy bank. On his twelfth birthday, he started saving money. Every week, on the first day of the week, he puts half of his $ 30 allowance into the bank. Write a formula for f(t), the amount of money in his piggy bank t days after his twelfth birthday, on the domain 0arrow_forwardA. Calculate each of the following limits, or explain why it does not converge. You may use any test to show that it doesn't converge. iii. limx → 1+ |x-1| / (x-1)2arrow_forwardCalculate each of the following limits, or explain why it does not converge.iii. limx → 1 |x-1| / (x-1)arrow_forwardUse the ratio test to determine whether an+1 lim n→∞ an (a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n ≥ 29, lim N→∞ - n=29 lim n→∞ = n5n (n + 2)! converges or diverges. (b) Evaluate the limit in the previous part. Enter ∞ as infinity and — ∞ as -infinity. If the limit does not exist, enter DNE. an+1 an (c) By the ratio test, does the series converge, diverge, or is the test inconclusive? Convergesarrow_forwardB. Calculate each of the following limits, or explain why it does not converge. You may use any theorems that were stated in lecture.iv. limx → 1+ |x-1| / (x-1)arrow_forwardUse the ratio test to determine whether an+1 lim n→∞ an (a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n ≥ 26, = lim n→∞ an ∞ n +8 n! lim n→∞ n=26 converges or diverges. (b) Evaluate the limit in the previous part. Enter ∞ as infinity and -∞ as -infinity. If the limit does not exist, enter DNE. an+1 0 (c) By the ratio test, does the series converge, diverge, or is the test inconclusive? Choosearrow_forwardQ4. Find the limitarrow_forwardThe following graph shows the approximate annual loss L(t) of XM Satellite Radio for the period 2001-2006 (t = 1 represents the start of 2001).+ XM Satellite Radio loss 800 600 400 200 3. 4 5 6. Year (a) What is the domain of L? (Enter your answer using interval notation.) [1,6] (b) Estimate L(2), L(4.5), and L(6). La500 700 L(2) = L(4.5) = L(6) = 300 Interpret your answers. nillion the vear2002 Loss ($ millions)arrow_forwardUse the ratio test to determine whether an+1 lim n→∞ an lim n→∞ (a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n ≥ 30, = lim n→∞ ∞ → = n=30 n² + 3 3n converges or diverges. (b) Evaluate the limit in the previous part. Enter ∞ as infinity and -∞ as -infinity. If the limit does not exist, enter DNE. an+1 an (c) By the ratio test, does the series converge, diverge, or is the test inconclusive? Choose ↑arrow_forwardUse the ratio test to determine whether an+1 lim n-x an = lim n→∞ n=24 (a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n > 24, n+8 n! converges or diverges. = (b) Evaluate the limit in the previous part. Enter ∞o as infinity and -∞o as -infinity. If the limit does not exist, enter DNE. an+1 lim n-x an (c) By the ratio test, does the series converge, diverge, or is the test inconclusive? Choosearrow_forwardA certain country's GDP (total monetary value of all finished goods and services produced in that country) can be approximated by g(t) = 3,000 – 560e-0.07t billion dollars per year (0 s t < 5), where t is time in years since January 2010. Find an expression for the total GDP G(t) of sold goods in this country from January 2010 to time t. HINT: [Use the shortcuts.] G(t) = Estimate, to the nearest billion dollars, the country's total GDP from January 2010 through June 2014. (The actual value was 11,376 billion dollars.) billion dollarsarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,