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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_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_forwardMultivariable Calculus Total Differentials and Approximations LIFE SCIENCE APPLICATIONS Heat Loss In Exercise 50 of Section 2 of this chapter, we found that the rate of heat loss in watts in harbor seal pups could be approximated by H(m,T,A)=15.2m0.67(TA)10.23lnm10.74 Where m is the body mass of the pup in kg, and T and A are the body core temperature and ambient water temperature, respectively in C. Suppose m is 25kg, T is 36.0, and A is 12.0, Approximate the change in H if m changes to 26kg,T to 36.5 and A to 10.0.arrow_forward
- Use 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_forwardPlant 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 OTHER APPLICATIONS Estimating Area The height of a triangle is measured as 37.5cm., with the base measured as 15.8cm. The measurement of the height can be off by as much as 0.8cm and that of the base by no more than 1.1cm. Estimate the maximum possible error in calculating the area of the triangle.arrow_forward
- Differentials: Linear Approximation For Exercises 1-8, find dyfor the given values of xand x. y=(2x-5)(x+1);x=2,x=-0.03arrow_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_forwardBlood Pressure The rate of change of the volume V(t) of blood in the aorta at time t is given by V(t)=kP(t), where P(t) is the pressure in the aorta at time t and k is a constant that depends upon properties of the aorta. The pressure in the aorta is given by P(t)=P0emt, where P0 is the pressure at time t=0 and m is another constant. Letting V0 be the volume at time t=0, find a formula for V(t).arrow_forward
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