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Solved: 1926. The Root Test Use the Root Test to determine whether the following series

Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs ISBN: 9780321947345 167

Solution for problem 21 Chapter 8.5

Calculus: Early Transcendentals | 2nd Edition

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Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs

Calculus: Early Transcendentals | 2nd Edition

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Problem 21

1926. The Root Test Use the Root Test to determine whether the following series converge. a _ k = 1 k2 2k

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Chapter 13: Translation and Proteins I. Uric Acid: a. Can build up and lead to Lesch-Nyhan disease b. Affected individuals have a symptom of self-mutilation c. To control this symptom, the individual may have their teeth removed so they can no longer chew holes in their cheeks, chew off their tongues, or chew down their fingers d. This is all due to a single gene mutation that leads to defective protein that leads to a phenotype II. Remember differences between prokaryotes and eukaryotes during protein synthesis (translation and transcription) a. Prokaryotes: no separation, can occur simultaneously b. Eukaryotes: separated, post transcription modification occur in the nucleus and then shipped out to cytoplasm where translation takes place c. These differences change how translation works, what happens and how we can regulate gene expression III. Ribosomes: the machines of protein synthesis. They consist of protein and RNA a. rRNA genes: make complexes with proteins, creases large and small subunits to make fully attached ready to go ribosomes b. Prokaryotes and Eukaryotes both have small and large subunits i. Eukaryotic subunits are larger in general than prokaryotes ii. Have to have BOTH subunits to be able to assemble a ribosome which is needed for translation to take place c. NOTE: understand that there are several working components that are coming together to help form the subunits which then form the ribosomes IV. Ribosomal RNAs: part of the machine for protein synthesis a. Ribosome: most abundant organelle in the cell b. Lethal if ribosome for the cell is not functionally properly or assembled correctly c. need a lot of rRNA and ribosomes to handle making all of the ribosomes when the cell needs them d. when they form the simple ribosome, made of the subunits, there are particular sites that are constant i. A, P, E 1. Where the tRNA interacts ii. mRNA binding site: where it binds to mRNA to be held V. Translation: divided into stages a. Charging: the binding of amino acids to tRNAs charges the ribosome i. Once tRNA is charged, it gets used and loses its charge. It then can be recharged and reused again. ii. Happens continuously throughout translation b. Initiation: what starts the whole process, getting the ribosome in the right location on mRNA c. Elongation: hooking together all of the amino acids d. Termination: stopping the process VI. tRNAs: can be modified and folded a. the shape they create is essential, have to fold correctly for the tRNA to work properly b. Anticodon: complementary and antiparallel to codon i. Recognized codon on mRNA c. Acceptor stem: grabs ahold of the amino acid VII. tRNA Charging: a. There is a tRNA for each amino acid i. NOTE: because of the wobble position, one tRNA picks up on several codons ii. See fewer than what would be calculated as possible b. Modification that tRNA can undergo: can create a modified base, creating a specialized base that will allow for it to recognize a C or a G i. Helps with the wobble c. All of these tRNAs have the same attachment site on top, it says “hey I need an amino acid” i. Amino acids cannot tell which tRNA is the correct one for them to bind to ii. Will use a key enzyme to direct the right amino acid to the right tRNA 1. Key enzyme: aminoacyl-tRNA synthetases******* a. ****** know this! 2. Different one for each amino acid, finds all of the tRNA that binds to a certain amino acid and then will connect them 3. tRNA is now charged, because it is holding onto an amino acid thanks to aminoacyl-tRNA synthetases 4. Uncharged: tRNA without an amino acid iii. Keep in mind: need charged tRNA to come into translation, becomes uncharged, then gets charged again. Allowing it to be used more than once VIII. Initiation of Translation a. Initiation: components assemble (mRNA, small and large subunits of ribosomes, initiation factors, initiator tRNA and GTP) b. Three major steps: i. mRNA binds to small ribosomal subunit ii. initiator tRNA binds to mRNA iii. Large ribosome subunit joins initiator complex c. IF-3: binds to the small subunit to keep the large subunit away. Stands for initiator factor 3. i. Allows for the small subunit to attach to the mRNA. ii. Helps the small subunit to find the Shine-Dalgarno sequence 1. Shine-Dalgarno Sequence: in bacteria transcripts. Essential in transcription a. Looks similar in every bacteria, can have some bases changes b. Interacts with rRNA of small subunit c. Can form hydrogen bonds d. Attaches small subunit in the correct position three bases away from the start codon i. Start codon: AUG ii. Shine-Dalgarno sequence is always in the same spot from the start codon, AUG iii. That way AUG is going to be lined up in what will fMet become the P site of the ribosome d. fMet-tRNA : i. the first fMet (the one before the –tRNA), says that it is a charged tRNA that is holding onto fMet. The fMet that is raised, says that this tRNA is supposed to hold onto fMet ii. if uncharged: tRNA fMet fMet iii. if messed up and charged incorrectly it could look like this: lys-tRNA 1. will read for fMet and then put down lys iv. fMet is special n-formyl methamine**** 1. prokaryotes have fMet for initiation, after that it is regular met 2. Eukaryotes have normal met 3. If you see fMet then you know it is a prokaryote IX. Elongation: a. Requires: i. 70S complex ii. Charged tRNAs iii. Elongation factors, GTP b. Initiator tRNA binds in the P site i. only where initiator tRNA will bind to c. During elongation, all tRNA will bind to the A site, then P site, then E site i. A, P, E d. Steps of Elongation: i. Delivery of a charged tRNA to A site ii. Peptide bond formation between AA in P and A, releases AA in P iii. Translocation: movement of ribosome down mRNA e. A, P, E are all three bases wide f. Peptidyl transferase: cuts amino acids in the P site, pasts it to amino acid in A site, forms peptide bond formation when it is pasted i. rRNA component, catalytic RNA or ribosome; carries out this activity g. The process: i. New charged tRNA goes into A site ii. Cuts amino acid from P site and then pastes it to A site iii. Scoots down or translocate iv. Repeat v. Peptide bonds form between amino acids vi. Creates polypeptide (connection of all the amino acids) h. Single charged tRNA comes into A site (one amino acid) i. Cut then transfer i. Very first amino acid is the farthest away j. Whatever three bases that are in the A site is the next codon k. ribosomes read RNA 5’ to 3’ i. Ribosome starts at the Shine-Dalgarno sequence ii. Reads 5’ to 3’ every three bases iii. Insertion or deletion will not stop this system 1. It cannot tell that there is a difference, will read the next three regardless X. Termination: a. No tRNA that matches the stop codons i. Instead of tRNA, a release factor will fill in the A site, will get cut and tried to be pasted, will not be pasted and the process will stop ii. Release factor will float away and the subunits break apart and releases the chain XI. Important parts of Transcription: a. Binding of amino acid to tRNA i. Amino acid: building blocks of proteins ii. tRNAs: what delivers the amino acid to the ribosomes iii. Aminoacyl-tRNA synthetase: attaches to amino acids to tRNA iv. ATP: provides energy for binding amino acid to tRNA b. Initiation i. mRNA: carries coding instructions ii. fMet-tRNA fMet: provides first amino acid in peptide iii. 30S ribosomal subunit (small subunit): attaches to mRNA iv. 50S ribosomal subunit (large subunit): stabilizes tRNAs and amino acids v. Initiator factor 1: enhances dissociation or large and small subunits of ribosome fMet vi. Initiator factor 2: binds GTP; delivers fMet-tRNA to initiation codon vii. Initiator factor 3***: binds to small subunit and prevents association with large subunit c. Elongation i. Ribosome: functional ribosome with A, P, and E sites where protein synthesis takes place ii. Charged tRNA: brings amino acids to ribosome and help assemble them in order specified by mRNA iii. Peptidyl transferase center: creates peptide bond between amino acids in A site and P site d. Termination: i. Release factors: bind to ribosome when stop codon is reached and terminate translation

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Chapter 8.5, Problem 21 is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 2
Author: William L. Briggs
ISBN: 9780321947345

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Solved: 1926. The Root Test Use the Root Test to determine whether the following series