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1. Show me what you know about monotonic sequences! a) What does it mean for a...
iro ha 2. Show me what you know about bounded sequences! a) What does it mean...
iro ha 2. Show me what you know about bounded sequences! a) What does it mean for a sequence to be bounded? Clearly state the definition using full sentences. A good start is, "A sequence {an) is bounded if and only if..." fra 10 b) Tell me in your own words what it means for a sequence to be bounded. Explain it as though I don't already know what this means, and you are teaching me. :) Ty
y, July AM 1. What does it mean for a sequence {a} to converge to a...
y, July AM 1. What does it mean for a sequence {a} to converge to a € R? State the definition (-1)+1 What about sequences that don't converge? Read the following proof by contradiction, and then complete Practice Question 6. Claim: {(-1)"} does not converge to any real number a. Proof: Assume that the sequence converges; that is, assume that there is an a E R such that lim,-(-1)" = a. Then, using & = 1, from the definition of...
1. What does it mean for a sequence {a} to converge to a € R? State...
1. What does it mean for a sequence {a} to converge to a € R? State the definition. (-1)n+1 2. Prove that lim = 0 n 2n 3. Prove that lim +0n + 1 = 2 80 4. Prove that lim +-+V5n 9 - 7 5. Prove that lim 108 + 137 13
4. Here is a fact about permutations: (*) nPr= n!/(n-k)!, for all k =n. Let's prove...
4. Here is a fact about permutations: (*) nPr= n!/(n-k)!, for all k =n. Let's prove this via mathematical induction for the fixed case k-3. 2 of 3 (i) Write clearly the statement (**) we wish to prove. Be sure your statement includes the phrase "for all n" (ii) State explicitly the assumption in (*) we will thus automatically make about k-2 (ii) Now recall that to prove by induction means to show that IfmPm!/lm-k)! is true for all km...
1. What can you predict about the location of core promoter sequences and polyadenylation cut sites...
1. What can you predict about the location of core promoter sequences and polyadenylation cut sites in the genomic sequence of a gene with multiple transcription start and termination sites?
Copy of Shown below is a plasmid containing several labeled sequences. Multi-cloning site (CS) Transcription terminator...
Copy of Shown below is a plasmid containing several labeled sequences. Multi-cloning site (CS) Transcription terminator Promoter TATA box original replication a) Based on the sequences it contains, is this plasmid intended for gene expression in eukaryotes or prokaryotes? How do you know? (3 pts) b) Based on your answer to part A, describe the promoter & terminator regions in a little more detail. What is a consensus sequence you would expect in the promoter? And what sorts of sequences...
What does it mean to 'solve a polynomial inequality'? What do you look for in the...
What does it mean to 'solve a polynomial inequality'? What do you look for in the original problem to know that it is indeed a polynomial inequality? What cues do you look for to help you get the solution process started? What might the solutions to the polynomial inequality look like? Include a specific example of at least one polynomial inequality. You may state the polynomial inequality only, no need to solve it. For example, "I know ... is a...
-(a) What does it mean to say that a sequence (an) is convergent, with limit L?...
-(a) What does it mean to say that a sequence (an) is convergent, with limit L? Show that, if x and 8 are real numbers with |2 – 11 < 8 and 0<83 1/2, then 1 – 2 Hence show that, if (an) is a convergent sequence of positive real numbers with limit 1, then (1/an) is also a convergent sequence with limit 1. (b) Suppose that (bk) is a sequence of real numbers such that, for each ke N,...
1. What does it mean for an allele to be dominant? (i.e. How do you know...
1. What does it mean for an allele to be dominant? (i.e. How do you know that Mendel's yellow seeds were considered dominant?) 2. In humans, apparently, the presence of dimples is a dominant characteristic. If the inheritance pattern of dimples is like that of pea color (i.e. two forms, dimples and no-dimples, one dominant and one recessive), described by Mendel, could non-dimpled parents give birth to a dimpled child? If non-dimpled parents do give birth to dimpled children, what...
please answer all questions and show all the work What does it mean for a sequence...
please answer all questions and show all the work
What does it mean for a sequence to converge? What does it mean for a series to converge? What does it mean for a series to converge absolutely? If a 2 Hint: There is no antiderivative of the standard normal curve, even of its easier-looking avatar e , that is expressible using elementary functions. But how then do we know there is any antiderivative of this function to speak of at...
iro ha 2. Show me what you know about bounded sequences! a) What does it mean for a sequence to be bounded? Clearly state the definition using full sentences. A good start is, "A sequence {an) is bounded if and only if..." fra 10 b) Tell me in your own words what it means for a sequence to be bounded. Explain it as though I don't already know what this means, and you are teaching me. :) Ty
y, July AM 1. What does it mean for a sequence {a} to converge to a € R? State the definition (-1)+1 What about sequences that don't converge? Read the following proof by contradiction, and then complete Practice Question 6. Claim: {(-1)"} does not converge to any real number a. Proof: Assume that the sequence converges; that is, assume that there is an a E R such that lim,-(-1)" = a. Then, using & = 1, from the definition of...
1. What does it mean for a sequence {a} to converge to a € R? State the definition. (-1)n+1 2. Prove that lim = 0 n 2n 3. Prove that lim +0n + 1 = 2 80 4. Prove that lim +-+V5n 9 - 7 5. Prove that lim 108 + 137 13
4. Here is a fact about permutations: (*) nPr= n!/(n-k)!, for all k =n. Let's prove this via mathematical induction for the fixed case k-3. 2 of 3 (i) Write clearly the statement (**) we wish to prove. Be sure your statement includes the phrase "for all n" (ii) State explicitly the assumption in (*) we will thus automatically make about k-2 (ii) Now recall that to prove by induction means to show that IfmPm!/lm-k)! is true for all km...
Copy of Shown below is a plasmid containing several labeled sequences. Multi-cloning site (CS) Transcription terminator Promoter TATA box original replication a) Based on the sequences it contains, is this plasmid intended for gene expression in eukaryotes or prokaryotes? How do you know? (3 pts) b) Based on your answer to part A, describe the promoter & terminator regions in a little more detail. What is a consensus sequence you would expect in the promoter? And what sorts of sequences...
-(a) What does it mean to say that a sequence (an) is convergent, with limit L? Show that, if x and 8 are real numbers with |2 – 11 < 8 and 0<83 1/2, then 1 – 2 Hence show that, if (an) is a convergent sequence of positive real numbers with limit 1, then (1/an) is also a convergent sequence with limit 1. (b) Suppose that (bk) is a sequence of real numbers such that, for each ke N,...
please answer all questions and show all the work
What does it mean for a sequence to converge? What does it mean for a series to converge? What does it mean for a series to converge absolutely? If a 2 Hint: There is no antiderivative of the standard normal curve, even of its easier-looking avatar e , that is expressible using elementary functions. But how then do we know there is any antiderivative of this function to speak of at...
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