1 answer

How do you use the integral test to determine whether #int x^-x# converges or diverges from #[1,oo)#?

Question:

How do you use the integral test to determine whether #int x^-x# converges or diverges from #[1,oo)#?

Answers

The integral:

#int_1^oo x^(-x)dx#

is convergent.

Explanation:

Based on the integral test, the convergence of the integral:

#int_1^oo x^(-x)dx#

is equivalent to the convergence of the series:

#sum_(n=1)^oo n^(-n)#

the series has positive terms and we can apply the root test:

#L = lim_(n->oo) root(n)(n^(-n)) = lim_(n->oo) (n^(-n))^(1/n) = lim_(n->oo) n^-1 = lim_(n->oo) 1/n = 0#

As #L < 1# the series is convergent and than also the integral is convergent.

.

Similar Solved Questions

1 answer
Calculate [H+] for each of the following solutions, and indicate whether the solution is acidic, basic,...
Calculate [H+] for each of the following solutions, and indicate whether the solution is acidic, basic, or neutral. 1.[OH−]= 8.0×10−9 M . Express your answer using two significant figures. 2.A solution in which [OH−] is 100 times greater than [H+]. Express your answer using t...
1 answer
Matlab Problem Plot the analytical and random walk solutions for concentration with D 0.01 att 1,...
Matlab Problem Plot the analytical and random walk solutions for concentration with D 0.01 att 1, 2, 5, and 10 s (four separate plots). Use an x-axis range from -2 to 2 and a y-axis range from 0 to 15e4 on all plots. Include the simulation end time in the plot title...
1 answer
Which of the following has had the greatest impact on your own life: race, gender, ethnicity,...
Which of the following has had the greatest impact on your own life: race, gender, ethnicity, or another characteristic? Which do you think is talked about more in today’s news stories and social media? How do you see this?...
1 answer
Using Rate of Return Analysis, determine the most economical alternative below. Assume a minimum ...
Using Rate of Return Analysis, determine the most economical alternative below. Assume a minimum attractive rate of retum of 696, and a 6-year life with no salvage value for each. The alternatives are mutually exclusive. Initial cost Annual Cost Annual Benefit IRR.% $3000,000 10000 120,300 18 $100,0...
1 answer
Constants Part A A positive point charge Q1-2.1 x 10-5 C is fixed at the origin...
Constants Part A A positive point charge Q1-2.1 x 10-5 C is fixed at the origin of coordinates, and a negative Find the location of the place(s) along the a axis where the electric field due to these two charges is zero point charge Q2 =-46 × 10-6 C is fixed to axis at -+2.5 m. Express your an...
1 answer
Using Python, Can someone please assist in the following: These are the hints: Summary This week's lab is to create a simple multiplication table using nested loops and if statements. Prompt the...
Using Python, Can someone please assist in the following: These are the hints: Summary This week's lab is to create a simple multiplication table using nested loops and if statements. Prompt the user for the size of the multiplication table (from 2x2 to 10x10). Use a validation loop to display...
1 answer
Ps & Awar Administrative Fello A Classification of Sc G Real Estate Licensing D Health Administratic...
ps & Awar Administrative Fello A Classification of Sc G Real Estate Licensing D Health Administratic Becoming a Classro D Saved Help Save r 02: Analyzing and Recording Transactions e debits and credits and explain double-entry accounting. wledge Check 04 fy whether each of these transactions wil...
1 answer
AyBridget Kanen is getting ready to open a small restaurant She is on a tight budget...
ayBridget Kanen is getting ready to open a small restaurant She is on a tight budget and must choose between the foliowing long-distance phone plans LPlan A: Pay 7 cents per minute of long-distance calling Dat Plan B: Pay a fixed monthly tee of S17 for up to 260 long-distance minutes and 5 cents per...
1 answer
Amber Mining and Milling, Inc., contracted with Truax Corporation to have constructed a custom-made lathe. The...
Amber Mining and Milling, Inc., contracted with Truax Corporation to have constructed a custom-made lathe. The machine was completed and ready for use on January 1, 2021. Amber paid for the lathe by issuing a $750,000, three-year note that specified 4% interest, payable annually on December 31 of ea...
1 answer
The rate constant for the first-order decomposition of a compound A in the reaction 2A rightarrow...
The rate constant for the first-order decomposition of a compound A in the reaction 2A rightarrow P is k = 3.6 times 10^-7 s^-1 at 25 degree C. What is the half-life of A? What will be the pressure, initially 33 kPa, at 50s, 20 min after initiation of the reaction?...
1 answer
8.5/17 D Sun 1133MQ F20 College Mathematics 10am De eerde Homework: Section 8.5 Homework Debby Cerda...
8.5/17 D Sun 1133MQ F20 College Mathematics 10am De eerde Homework: Section 8.5 Homework Debby Cerda & ! 09/14/10 2:33 AM Score: 0 of 1 pt 17 of 21 (10 complete HW Score: 40%. 8.4 of 21 pts 8.5.41 Question Help o Rihanna took out a 4-year amortired loan for $22.000 at 12% to pay heronta cons...
1 answer
The following table gives the free throws attempted (FTA) and the free throws made (FTM) for the top five players in the NBA for a recent season
Statistics. The following table gives the free throws attempted (FTA) and the freethrows made (FTM) for the top five players in the NBA for a recent season. Calculatethe free throw percentage for each player by writing the FTM over the FTAand converting this fraction to a decimal.Player- FTM FTAAlla...
1 answer
Consider a CAN system. We use the bit time for time unit, i.e., one time unit is the time needed to transmit one bit. The longest propagation delay is two time units. Two nodes, A, and B, are trying t...
Consider a CAN system. We use the bit time for time unit, i.e., one time unit is the time needed to transmit one bit. The longest propagation delay is two time units. Two nodes, A, and B, are trying to access the bus at time 0. Node C tries to access the bus at time 5. The identifier for node A is: ...
1 answer
Lead(II) sulfate is the crust that forms on battery terminals, its solubility in water is 0.00425...
Lead(II) sulfate is the crust that forms on battery terminals, its solubility in water is 0.00425 g/ 100 mL. If 20.0 kg of lead(II) sulfate has been stored of in a 100 L tank filled with water what is the concentration of Pb2+ in the water? (KSP = 6.3 x 10-7, MW = 303.26 g/mol)...