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L'Hôpital's Rule does not help with the limit in this exercise. Try it, and you will just keep on cycling. Find the limit some other way. limx→∞ e^x5/3xe^x limx→∞ e^x5/3xe^x = (Simplify your answer.)

L'Hôpital's Rule does not help with the limit in this exercise. Try it, and you will just keep on cycling. Find the limit some other way. limx→∞ e^x5/3xe^x limx→∞ e^x5/3xe^x = (Simplify your answer.)

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L'Hôpital's Rule does not help with the limit in this exercise. Try it, and you will just keep on cycling. Find the limit some other way. limx→∞ e^x5/3xe^x limx→∞ e^x5/3xe^x = (Simplify your answer.)

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Grading for Numeric Answers Tolerance Some numeric answers to questions need to be exact. For example, the answer to the question "How many days are in a week?" must be exactly 7. In general though, numeric answers are graded as correct if they fall within an acceptable range (or tolerance) of the official correct answer. For example, if the answer to a numeric problem with a tolerance of 2% was 105, then entering any value between approximately 103 and 107 would be graded as correct, as shown in the region shaded green below. The typical grading tolerance in Mastering is 2-3%, although this value may vary (e.g. more lenient) depending on the particular problem. A number line is marked at 100, 105, and 110, where 105 is the properly-rounded answer. A green shaded region extends beyond 105 by 2 percent of this value in each direction. Significant Figures While Mastering does not directly grade your answer based on the number of significant figures it contains, the tolerance mentioned above is centered around the properly-rounded answer (as opposed to the full-precision answer). In some problems you will be explicitly told how many significant figures your answer should contain. You may find that entering extra significant figures than required often causes your answer to still fall within the accepted tolerance and thus graded as correct. However, there are problems where not rounding properly may cause your answer to fall outside the accepted tolerance, so it's important to follow the general rules for significant figures, as the following example illustrates. Suppose you are asked to find the area of a rectangle that is 3.1 cm wide and 4.4 cm long. The full-precision answer from your calculator would be 13.64 cm2, although given the rules for significant figures, this answer should be rounded to two significant figures before being entered, or 14 cm2. If you were to enter 13.64 cm2, it would not be graded as correct since this value falls outside the 2% tolerance of the properly-rounded answer of 14 cm2. Instead, you would receive feedback from Mastering telling you to check the rounding of your final answer, although you would not be deducted any points. Part A What is the area of a rectangle that is 3.1 cm wide and 4.4 cm long? Enter the full-precision answer first to see the corresponding feedback before entering the properly-rounded answer. (You do not need to enter the units in this case since they are provided to the right of the answer box). Part B Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.) Part C The momentum of an object is determined to be 7.2×10-3 kg⋅m/s. Express this quantity as provided or use any equivalent unit. (Note: 1 kg = 1000 g). Part D Enter the following expression in the answer box below: √2gλ3m, where λ is the lowercase Greek letter lambda.Grading for Numeric Answers Tolerance Some numeric answers to questions need to be exact. For example, the answer to the question "How many days are in a week?" must be exactly 7. In general though, numeric answers are graded as correct if they fall within an acceptable range (or tolerance) of the official correct answer. For example, if the answer to a numeric problem with a tolerance of 2% was 105, then entering any value between approximately 103 and 107 would be graded as correct, as shown in the region shaded green below. 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Enter the full-precision answer first to see the corresponding feedback before entering the properly-rounded answer. (You do not need to enter the units in this case since they are provided to the right of the answer box). Part B Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.) Part C The momentum of an object is determined to be 7.2×10-3 kg⋅m/s. Express this quantity as provided or use any equivalent unit. (Note: 1 kg = 1000 g). Part D Enter the following expression in the answer box below: √2gλ3m, where λ is the lowercase Greek letter lambda.Grading for Numeric Answers Tolerance Some numeric answers to questions need to be exact. For example, the answer to the question "How many days are in a week?" must be exactly 7. 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Part D Enter the following expression in the answer box below: √2gλ3m, where λ is the lowercase Greek letter lambda.Grading for Numeric Answers Tolerance Some numeric answers to questions need to be exact. For example, the answer to the question "How many days are in a week?" must be exactly 7. In general though, numeric answers are graded as correct if they fall within an acceptable range (or tolerance) of the official correct answer. For example, if the answer to a numeric problem with a tolerance of 2% was 105, then entering any value between approximately 103 and 107 would be graded as correct, as shown in the region shaded green below. The typical grading tolerance in Mastering is 2-3%, although this value may vary (e.g. more lenient) depending on the particular problem. A number line is marked at 100, 105, and 110, where 105 is the properly-rounded answer. A green shaded region extends beyond 105 by 2 percent of this value in each direction. Significant Figures While Mastering does not directly grade your answer based on the number of significant figures it contains, the tolerance mentioned above is centered around the properly-rounded answer (as opposed to the full-precision answer). In some problems you will be explicitly told how many significant figures your answer should contain. You may find that entering extra significant figures than required often causes your answer to still fall within the accepted tolerance and thus graded as correct. However, there are problems where not rounding properly may cause your answer to fall outside the accepted tolerance, so it's important to follow the general rules for significant figures, as the following example illustrates. Suppose you are asked to find the area of a rectangle that is 3.1 cm wide and 4.4 cm long. 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The typical grading tolerance in Mastering is 2-3%, although this value may vary (e.g. more lenient) depending on the particular problem. A number line is marked at 100, 105, and 110, where 105 is the properly-rounded answer. A green shaded region extends beyond 105 by 2 percent of this value in each direction. Significant Figures While Mastering does not directly grade your answer based on the number of significant figures it contains, the tolerance mentioned above is centered around the properly-rounded answer (as opposed to the full-precision answer). In some problems you will be explicitly told how many significant figures your answer should contain. You may find that entering extra significant figures than required often causes your answer to still fall within the accepted tolerance and thus graded as correct. However, there are problems where not rounding properly may cause your answer to fall outside the accepted tolerance, so it's important to follow the general rules for significant figures, as the following example illustrates. Suppose you are asked to find the area of a rectangle that is 3.1 cm wide and 4.4 cm long. The full-precision answer from your calculator would be 13.64 cm2, although given the rules for significant figures, this answer should be rounded to two significant figures before being entered, or 14 cm2. If you were to enter 13.64 cm2, it would not be graded as correct since this value falls outside the 2% tolerance of the properly-rounded answer of 14 cm2. Instead, you would receive feedback from Mastering telling you to check the rounding of your final answer, although you would not be deducted any points. Part A What is the area of a rectangle that is 3.1 cm wide and 4.4 cm long? Enter the full-precision answer first to see the corresponding feedback before entering the properly-rounded answer. (You do not need to enter the units in this case since they are provided to the right of the answer box). Part B Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.) Part C The momentum of an object is determined to be 7.2×10-3 kg⋅m/s. Express this quantity as provided or use any equivalent unit. (Note: 1 kg = 1000 g). Part D Enter the following expression in the answer box below: √2gλ3m, where λ is the lowercase Greek letter lambda.
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2 0

Mindset is an idea proposed by Stanford University psychologist Carol Dweck based on her research in motivation and development. According to Dweck, people generally have a tendency to think with one of two different mindsets: a fixed mindset or a growth mindset. As you start this semester, it can be useful to think about some ideas and strategies that will help you to succeed. In these materials, we will describe some ideas about motivation, based on cutting-edge research, and offer some suggestions for how to get the most out of Mastering and your course. Watch the following videos and answer the accompanying questions to learn more. Do You Have a Growth Mindset? Part A Which of the following describes a growth mindset, as opposed to a fixed mindset? 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Mindset is an idea proposed by Stanford University psychologist Carol Dweck based on her research in motivation and development. According to Dweck, people generally have a tendency to think with one of two different mindsets: a fixed mindset or a growth mindset. As you start this semester, it can be useful to think about some ideas and strategies that will help you to succeed. In these materials, we will describe some ideas about motivation, based on cutting-edge research, and offer some suggestions for how to get the most out of Mastering and your course. Watch the following videos and answer the accompanying questions to learn more. Do You Have a Growth Mindset? Part A Which of the following describes a growth mindset, as opposed to a fixed mindset? 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Solution
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Consider the circuit shown in Figure 2 below, with gm1 = 100 mA/V, gm2 = 20 mA/V, gm3 = 3 mA/V, R1 = 2 kΩ, R2 = 1 kΩ, VDD = 5 V, and all NMOS devices are in saturation. Channel length modulation and the body effect should be ignored for this problem. (And, hopefully, it is obvious that gm1, gm2, and gm3 correspond to the device transconductances of NMOS devices M1, M2, and M3, respectively: if this wasn't obvious, note that the next time you see something like this, I probably won't spell it out for you so explicitly. if at all, so please make a mental note of these kinds of things.) a) Determine the numerical small-signal voltage gain: i) Av = Vout/Vin in units of V/V and ii) |Av| in units of dB. Be sure to indicate whether your numerical answers are positive-valued or negative-valued (numerical answers with ambiguous signs will receive little, if any: credit, partial or otherwise). List your numerical answers in proper engineering notation format with appropriate units, and show your work. b) Determine the numerical small-signal resistance "seen" looking into node Vin. List your numerical answer in proper engineering notation format with appropriate units, and show your work. c) Determine the numerical small-signal resistance "seen" looking into node Vx. List your numerical answer in proper engineering notation format with appropriate units, and show your work. d) Determine the numerical small-signal resistance "seen" looking into node Vy. List your numerical answer in proper engineering notation format with appropriate units, and show your work. e) Determine the numerical small-signal resistance "seen" looking into node Vout. List your numerical answer in proper engineering notation format with appropriate units. and show your work.
Solution
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