![Even innocent looking calculus problems can lead to overflow. a. (10 points) Show that the maximum value of the function f(x)- greater than 10124 25 is (1.0001) b. (5 points) what is the limit off(x) as x->o? Hint: Use logarithms.]](http://img.homeworklib.com/questions/54ce2e60-2968-11ec-bc6a-75088a57ad6c.png?x-oss-process=image/resize,w_560)
Homework Answers
![(b) To find the limit of f(x) as x → 25 11m 25lnx Apply LHospital Rule] 11m x-200Lx ln( 1.0001) 25 11mln (10001) [Apply LHos](http://img.homeworklib.com/questions/dfef5d10-2969-11ec-a0aa-e106efc336f0.png?x-oss-process=image/resize,w_560)
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Even innocent looking calculus problems can lead to overflow. a. (10 points) Show that the maximum...
please prove part (b) use complex analysis and calculus of residue -dx neif a> 0 5....
please prove part (b) use complex analysis and calculus of
residue
-dx neif a> 0 5. (a) x2+1 (b) For any real number a > 0, cos x dx ne"/a. a Hint: This is the real part of the integral obtained by replacing cos x by e
Show your work and give clear explanations and proofs in all problems. If you use a...
Show your work and give clear explanations and proofs in all
problems. If you use a theorem, state the theorem
3. (34 pts) Assume that (an) is a sequence in R and an > 0 for all n in N. Prove that if an converges, then n+1 also converges. nel
WHILE LOOPS (13 points) Write a MATLAB program to find the smallest integer N such that:...
WHILE LOOPS (13 points) Write a MATLAB program to find the smallest integer N such that: i> limit For example, if the limit is 5, the smallest N would be 3 since 1 + 2 + 3 = 6, and 6 > 5. If the limit is 15, the smallest N is 6 because 1+ 2+ 3+ 4+ 5+ 6 = 21. Note that N is not 5 in this case because 1+ 2+ 3+ 4+ 5 = 15, and...
Problem 10 (9 points) The lifetime (in hours) of a replacement part for a machine is...
Problem 10 (9 points) The lifetime (in hours) of a replacement part for a machine is modeled as having a Weibull distribution with parameters a- V2 and ß 20. 2pts i. What are the mean and standard deviation of this Weibull distribution? σ= (round to nearest integer) 2pts . Determine the probability that a single replacement part provides over 25 hours of operation for the machine. P(X > 25) iii. We currently have a supply of 49 replacement parts. Use...
2. Recap: Maximum Likelihood Estimators and Fisher information Bookmark this page Instructions: For each of the...
2. Recap: Maximum Likelihood Estimators and Fisher information Bookmark this page Instructions: For each of the following distributions, compute the maximum likelihood estimator based on n i.i.d. observations X1,..., Xn and the Fisher information, if defined. If it is not enter DNE in each applicable input box. (d) 7 points possible (graded) X; ~N (u,0?), u ER, o? > 0, which means that each X1 has density Hint: Keep in mind that we consider o? as the parameter, not o....
Problem 1 (16 points). Suppose that Y is normally distributed random variable with u-10 and σ-2...
Problem 1 (16 points). Suppose that Y is normally distributed random variable with u-10 and σ-2 and X is another normally distributed random variable with μ-: 5 and σ-5. Y and X are independent. Calculate the following probabilities according to a normal distribution table (e.g., a normal table found from the Internet) (1) (4 points) Pr(Y> 12) (2) (4 points) Pr(2 < X <4) (3) (4 points) Pr(Y> 12 and 2< X <4) and Pr(Y> 12 or 2< X <4)...
Problem 7.1 (10 points) Express the unilateral z-transforms of the following functions as rational functions. Find...
Problem 7.1 (10 points) Express the unilateral z-transforms of the following functions as rational functions. Find also the ROC. You may use tables. (a) xl[n]-1-0.2)" (b) x2[n] (0.3)" +2(-5) -0.2n Problem 7.2 (10 points) Express the unilateral z-transforms of the following functions as rational functions. Find also the ROC. You may use tables. (a) xl[n] = 3e-j02" (b) x2[n]- 5cos(5n) (c) x3[n] = e-0.gn sin(0.7n) Problem 7.3 (10 points) The signals given are sampled every 0.3 s, beginning att-0. Find...
For Problems 5 to 6: Figure shows a capacitor connected to a voltage source. There are...
For Problems 5 to 6: Figure shows a capacitor connected to a voltage source. There are two dielectric slabs stacked in the capacitor. The dielectric slabs are not perfect dielectrics, thus they have finite conductivities. Hint: Notice that electric flux densities in dielectrics 1 and 2 are equal: D-D2 Another hint: You can imagine this structure as two capacitors connected in series. Can you find the voltage Kon capacitor 1. V-4cos(at),o-10,ad /sec, w-o1m, 1:0.ln?, ,-3,e,2-5, ?,-100,?,-200,di-d,-0.002m 82,02 Problem [51 <15...
Algorithm Humble Numbers Problem 4-1 (Humble Numbers) 10 points A number k > 1 is called...
Algorithm
Humble Numbers
Problem 4-1 (Humble Numbers) 10 points A number k > 1 is called humble if the only prime factors of k are 3 and 5. Consider the task of on input n, outputting the n smallest humble numbers and the following algorithm to do it: HuMBLE(n) count = 0. pret,Output = 0 HEAP.INSERT (3) HEAP.INSERT (5) while (count < n) cur - HEAP. EXTRACTMIN if cur prevOutput then output cur HEAP,INSERT(3*cur) HEAP.İNSERT(5*cur) count -count+1 preu,Output = cur...
7 The publisher of a sports magazine plans to offer new subscribers one of three gifts:...
7 The publisher of a sports magazine plans to offer new subscribers one of three gifts: a sweatshirt with the logo of their favorite team, a coffee cup with the logo of their favorite team, or a pair of earrings also with the logo of their favorite team. In a sample of 431 new subscribers, the number selecting each gift is reported below. At the 0.02 significance level, is there a preference for the gifts or should we conclude that...
please prove part (b) use complex analysis and calculus of
residue
-dx neif a> 0 5. (a) x2+1 (b) For any real number a > 0, cos x dx ne"/a. a Hint: This is the real part of the integral obtained by replacing cos x by e
Show your work and give clear explanations and proofs in all
problems. If you use a theorem, state the theorem
3. (34 pts) Assume that (an) is a sequence in R and an > 0 for all n in N. Prove that if an converges, then n+1 also converges. nel
WHILE LOOPS (13 points) Write a MATLAB program to find the smallest integer N such that: i> limit For example, if the limit is 5, the smallest N would be 3 since 1 + 2 + 3 = 6, and 6 > 5. If the limit is 15, the smallest N is 6 because 1+ 2+ 3+ 4+ 5+ 6 = 21. Note that N is not 5 in this case because 1+ 2+ 3+ 4+ 5 = 15, and...
Problem 10 (9 points) The lifetime (in hours) of a replacement part for a machine is modeled as having a Weibull distribution with parameters a- V2 and ß 20. 2pts i. What are the mean and standard deviation of this Weibull distribution? σ= (round to nearest integer) 2pts . Determine the probability that a single replacement part provides over 25 hours of operation for the machine. P(X > 25) iii. We currently have a supply of 49 replacement parts. Use...
2. Recap: Maximum Likelihood Estimators and Fisher information Bookmark this page Instructions: For each of the following distributions, compute the maximum likelihood estimator based on n i.i.d. observations X1,..., Xn and the Fisher information, if defined. If it is not enter DNE in each applicable input box. (d) 7 points possible (graded) X; ~N (u,0?), u ER, o? > 0, which means that each X1 has density Hint: Keep in mind that we consider o? as the parameter, not o....
Problem 1 (16 points). Suppose that Y is normally distributed random variable with u-10 and σ-2 and X is another normally distributed random variable with μ-: 5 and σ-5. Y and X are independent. Calculate the following probabilities according to a normal distribution table (e.g., a normal table found from the Internet) (1) (4 points) Pr(Y> 12) (2) (4 points) Pr(2 < X <4) (3) (4 points) Pr(Y> 12 and 2< X <4) and Pr(Y> 12 or 2< X <4)...
Problem 7.1 (10 points) Express the unilateral z-transforms of the following functions as rational functions. Find also the ROC. You may use tables. (a) xl[n]-1-0.2)" (b) x2[n] (0.3)" +2(-5) -0.2n Problem 7.2 (10 points) Express the unilateral z-transforms of the following functions as rational functions. Find also the ROC. You may use tables. (a) xl[n] = 3e-j02" (b) x2[n]- 5cos(5n) (c) x3[n] = e-0.gn sin(0.7n) Problem 7.3 (10 points) The signals given are sampled every 0.3 s, beginning att-0. Find...
For Problems 5 to 6: Figure shows a capacitor connected to a voltage source. There are two dielectric slabs stacked in the capacitor. The dielectric slabs are not perfect dielectrics, thus they have finite conductivities. Hint: Notice that electric flux densities in dielectrics 1 and 2 are equal: D-D2 Another hint: You can imagine this structure as two capacitors connected in series. Can you find the voltage Kon capacitor 1. V-4cos(at),o-10,ad /sec, w-o1m, 1:0.ln?, ,-3,e,2-5, ?,-100,?,-200,di-d,-0.002m 82,02 Problem [51 <15...
Algorithm
Humble Numbers
Problem 4-1 (Humble Numbers) 10 points A number k > 1 is called humble if the only prime factors of k are 3 and 5. Consider the task of on input n, outputting the n smallest humble numbers and the following algorithm to do it: HuMBLE(n) count = 0. pret,Output = 0 HEAP.INSERT (3) HEAP.INSERT (5) while (count < n) cur - HEAP. EXTRACTMIN if cur prevOutput then output cur HEAP,INSERT(3*cur) HEAP.İNSERT(5*cur) count -count+1 preu,Output = cur...
7 The publisher of a sports magazine plans to offer new subscribers one of three gifts: a sweatshirt with the logo of their favorite team, a coffee cup with the logo of their favorite team, or a pair of earrings also with the logo of their favorite team. In a sample of 431 new subscribers, the number selecting each gift is reported below. At the 0.02 significance level, is there a preference for the gifts or should we conclude that...
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