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LIFE SCIENCE APPLICATIONS
Heat Loss In Exercise
Where
ambient water temperature, respectively (in
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Calculus For The Life Sciences
- Multivariable Calculus Total Differentials and Approximations LIFE SCIENCE APPLICATIONS Blood Volume In Exercise 52 of Section 2 in this chapter, we found that the number of liters of blood pumped through the lungs in one minute is given by C=bav Suppose a=160,b=200 and v=125. Estimate the change in C if a becomes 145,b becomes 190, and v changes to 130.arrow_forwardUse the total differential to approximate each quantity. Then use a calculator to approximate the quantity, and give the absolute value of the differences in the two results to 4decimal places. 0.98e0.04.arrow_forwardUse the differential to approximate each quantity. Then use a calculator to approximate the quantity, and give the absolute value of the difference the two results to 4decimal places. e0.002arrow_forward
- Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be described by the differential equation dPdR=4DRP2 where D is the density of the plants in an area. Source: Ecology. Given the initial condition P(0)=1, find a formula for P in term of R.arrow_forwardMultivariable Calculus Total Differentials and Approximations LIFE SCIENCE APPLICATIONS Horn Volume The volume of the horns from bighorn sheep was estimated by researchers using the equation V=h3(r21+r1r2+r22) where h is the length of a horn segment in centimeters and r1 and r2 are the radii of the two ends of the horn segment in centimeters. Source: Conservation Biology. a. Determine the volume of the segment of horn that is 40cm long with radii of 5cm and 3cm, respectively. b. Use the total differential to estimate the volume of the segment of horn if the horn segment from part a was actually 42cm long with radii of 5.1cm and 2.9cm, respectively. Compare this with the actual volume.arrow_forwardVelocity A car is moving along a straight test track. The position in feet of the car, s(t), at various times t is measured, with the following results. Find and interpret the average velocities for the following changes in t. a. 0to2seconds b. 2to4seconds c. 4to6seconds d. 6to8seconds e. Estimate the instatneous velocity at 4 seconds. i. by finding the average velocity between 2 and 6 seconds, and ii. by averageing the answers for the average velocity in the two seconds before and the two seconds after that is, the answers to parts b and c. f. Estimate the instantaneous velocity at 6 seconds using the two methods in part e. g. Notice in parts e and f that your two answers are the same. Discuss whether this will always be the case, and why or why not.arrow_forward
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