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Kailash Paw

Kailash P.

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In Exercises $11-22,$ estimate the minimum number of subintervals needed to approximate the integrals with an error of magnitude less than $10^{-4}$ by (a) the Trapezoidal Rule and (b) Simpson's Rule. (The integrals in Exercises $11-18$ are the integrals from Exercises $1-8 .$ ) $$\int_{-2}^{0}\left(x^{2}-1\right) d x$$

In Exercises $11-22,$ estimate the minimum number of subintervals needed to approximate the integrals with an error of magnitude less than $10^{-4}$ by (a) the Trapezoidal Rule and (b) Simpson's Rule. (The integrals in Exercises $11-18$ are the integrals from Exercises $1-8 .$ ) $$\int_{-2}^{0}\left(x^{2}-1\right) d x$$

University Calculus: Early Transcendentals

Techniques of Integration

Numerical Integration

The marginal cost function $C^{\prime}(x)$ was defined to be the derivative of the cost function. (See Sections 3.8 and $4.6 .$ ) If the marginal cost of manufacturing $x$ meters of a fabric is $C^{\prime}(x)=5-0.008 x+0.000009 x^{2}$ (measured in dollars per meter) and the fixed start-up cost is $C(0)=\$ 20.000 .$ use the Net Change Theorem to find the cost of producing the first 2000 units.

Calculus

Applications of Integration

Applications to Economics and Biology
A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after $ t $ minutes. When the data in the table are graphed, the slope of the tangent line represents the heart rate in beats per minute. $$ \begin{array}{|l|c|c|c|c|c|} \hline t \text { (min) } & 36 & 38 & 40 & 42 & 44 \\ \hline \text { Heartbeats } & 2530 & 2661 & 2806 & 2948 & 3080 \\ \hline \end{array} $$ The monitor estimates this value by calculating the slope of a secant line. Use the data to estimate the patient's heart rate after 42 minutes using the secant line between the points with the given values of $ t $. (a) $ t = 36 $ and $ t = 42 $ (b) $ t = 38 $ and $ t = 42 $ (c) $ t = 40 $ and $ t = 42 $ (d) $ t = 42 $ and $ t = 44 $ What are your conclusions?

A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after $ t $ minutes. When the data in the table are graphed, the slope of the tangent line represents the heart rate in beats per minute. $$ \begin{array}{|l|c|c|c|c|c|} \hline t \text { (min) } & 36 & 38 & 40 & 42 & 44 \\ \hline \text { Heartbeats } & 2530 & 2661 & 2806 & 2948 & 3080 \\ \hline \end{array} $$ The monitor estimates this value by calculating the slope of a secant line. Use the data to estimate the patient's heart rate after 42 minutes using the secant line between the points with the given values of $ t $. (a) $ t = 36 $ and $ t = 42 $ (b) $ t = 38 $ and $ t = 42 $ (c) $ t = 40 $ and $ t = 42 $ (d) $ t = 42 $ and $ t = 44 $ What are your conclusions?

Calculus: Early Transcendentals

Limits and Derivatives

The Tangent and Velocity Problems
A rough-surfaced turntable mounted on frictionless bearings initially rotates at 1.8 rev/s about its vertical axis. The rotational inertia of the turntable is $0.020 \mathrm{kg} \cdot \mathrm{m}^{2} . \mathrm{A} 200-\mathrm{g}$ lump of putty is dropped onto the turntable from 0.0050 $\mathrm{m}$ above the turntable and at a distance of 0.15 $\mathrm{m}$ from its axis of rotation. The putty adheres to the surface of the turntable. (a) Find the initial kinetic energy of the turntable. (b) What is the final rotational speed of the system (the lump of putty and turntable)? (c) What is the final linear speed of the lump of putty? Find the change in kinetic energy of (d) the turntable, (e) the putty, and (f) the putty-turntable combination. How do you account for your answers?

A rough-surfaced turntable mounted on frictionless bearings initially rotates at 1.8 rev/s about its vertical axis. The rotational inertia of the turntable is $0.020 \mathrm{kg} \cdot \mathrm{m}^{2} . \mathrm{A} 200-\mathrm{g}$ lump of putty is dropped onto the turntable from 0.0050 $\mathrm{m}$ above the turntable and at a distance of 0.15 $\mathrm{m}$ from its axis of rotation. The putty adheres to the surface of the turntable. (a) Find the initial kinetic energy of the turntable. (b) What is the final rotational speed of the system (the lump of putty and turntable)? (c) What is the final linear speed of the lump of putty? Find the change in kinetic energy of (d) the turntable, (e) the putty, and (f) the putty-turntable combination. How do you account for your answers?

College Physics

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( int sqrt{49-x^{2}} d x )

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The evolution of whales from a 4-legged ancestor is an example of microevolution that can be seen in the changes in the gene pool. True False

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Matching (A) Fossils (B) Molecular DNA (C) Embryology (D) Biogeography (E) Comparative Anatomy (F) Direct Evidence

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Allele Frequency Analysis A small population of rare flowers is being studied in one area. Scientists look at two alleles - "T" for tall and "t" for short. The following chart gives the TOTAL NUMBER of flowers with each genotype during a study that lasted 10 generations: egin{tabular}{|l|c|c|c|} hline & TT & ( mathrm{Tt} ) & ( mathrm{tt} ) \ hline First Generation & 40 & 30 & 30 \ hline Fifth Generation & 60 & 20 & 20 \ hline Tenth Generation & 70 & 20 & 10 \ hline end{tabular}

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Marisa A verified

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Allele Frequency Analysis A small population of rare flowers is being studied in one area. Scientists look at two alleles - "T" for tall and "t" for short. The following chart gives the TOTAL NUMBER of flowers with each genotype during a study that lasted 10 generations: egin{tabular}{|l|c|c|c|} hline & TT & ( mathrm{Tt} ) & ( mathrm{tt} ) \ hline First Generation & 40 & 30 & 30 \ hline Fifth Generation & 60 & 20 & 20 \ hline Tenth Generation & 70 & 20 & 10 \ hline end{tabular}

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Katlin Koehn verified

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(A) (B) (c) (D)

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(A) (B) (C) (D)

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The fin of a dolphin and the fin of a fish have similar functions (for swimming), but the internal structure of the fins are very different. Though both are vertebrates, dolphins are mammals and fish are not. These two fins are a result of _______________ evolution. convergent divergent random homologous

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Marisa A verified

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Finch Phylogenetic Tree

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Katlin Koehn verified

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Finch Phylogenetic Tree

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