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Calculus For The Life Sciences
2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: Pearson Addison Wesley,
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Question
Chapter 4.4, Problem 18E
To determine
To find:
The derivative of the function y=ex2x+1
Expert Solution & Answer
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Students have asked these similar questions
This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one.
A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The
wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture.
A
B
A
B
at some instant, the piston will be tangent to the circle
(a) Express the x and y coordinates of point A as functions of t:
x= 2 cos(3πt)
and y= 2 sin(3t)
(b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds:
-cot(3πt)
sin(3лt)
(c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411-
4
-2 sin (3лt)
(d)…
5. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.AE.003.
y
y= ex²
0
Video Example
x
EXAMPLE 3
(a) Use the Midpoint Rule with n = 10 to approximate the integral
कर
L'ex²
dx.
(b) Give an upper bound for the error involved in this approximation.
SOLUTION
8+2
1
L'ex² d
(a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.)
dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)]
0.1 [0.0025 +0.0225
+
+ e0.0625 + 0.1225
e0.3025 + e0.4225
+ e0.2025
+
+ e0.5625 €0.7225 +0.9025]
The figure illustrates this approximation.
(b) Since f(x) = ex², we have f'(x)
=
0 ≤ f'(x) =
< 6e.
ASK YOUR TEACHER
and f'(x) =
Also, since 0 ≤ x ≤ 1 we have x² ≤
and so
Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final
answer to five decimal places.)
6e(1)3
e
24(
=
≈
2. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.015.
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.)
ASK YOUR TEACHER
3
1
3 +
dy, n = 6
(a) the Trapezoidal Rule
(b) the Midpoint Rule
(c) Simpson's Rule
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Chapter 4 Solutions
Calculus For The Life Sciences
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Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Find the derivative of each function. y=log74x-3Ch. 4.5 - Find the derivative of each function....Ch. 4.5 - Find the derivative of each function....Ch. 4.5 - Prob. 39ECh. 4.5 - Find the derivative of each function. z=10ylogyCh. 4.5 - Prob. 41ECh. 4.5 - Find the derivative of each function. fx=lnxex+2Ch. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Prob. 45ECh. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Use a graphing calculator to sketch the graph of...Ch. 4.5 - Prob. 49ECh. 4.5 - Prob. 50ECh. 4.5 - Prob. 51ECh. 4.5 - Prob. 52ECh. 4.5 - Prob. 53ECh. 4.5 - Prob. 54ECh. 4.5 - Prob. 55ECh. 4.5 - This exercise shows another way to derive the...Ch. 4.5 - Prob. 57ECh. 4.5 - Population Growth Suppose that the population of a...Ch. 4.5 - Body Surface Area There is a mathematical...Ch. 4.5 - Prob. 60ECh. 4.5 - Prob. 61ECh. 4.5 - Fruit Flies A study of the relation between the...Ch. 4.5 - Prob. 63ECh. 4.5 - Poverty The passage of the Social Security...Ch. 4.5 - 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Prob. 36CRCh. 4.CR - Prob. 37CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 39CRCh. 4.CR - Prob. 40CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 42CRCh. 4.CR - Prob. 43CRCh. 4.CR - Prob. 44CRCh. 4.CR - Prob. 45CRCh. 4.CR - Prob. 46CRCh. 4.CR - Prob. 47CRCh. 4.CR - Prob. 48CRCh. 4.CR - Prob. 49CRCh. 4.CR - Prob. 50CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 52CRCh. 4.CR - Prob. 53CRCh. 4.CR - Prob. 54CRCh. 4.CR - Prob. 55CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 57CRCh. 4.CR - Prob. 58CRCh. 4.CR - Prob. 59CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 61CRCh. 4.CR - Prob. 62CRCh. 4.CR - Prob. 63CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 65CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 68CRCh. 4.CR - Consider the following table of values of the...Ch. 4.CR - 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- practice problem please help!arrow_forwardFind a parameterization for a circle of radius 4 with center (-4,-6,-3) in a plane parallel to the yz plane. Write your parameterization so the y component includes a positive cosine.arrow_forward~ exp(10). A 3. Claim number per policy is modelled by Poisson(A) with A sample x of N = 100 policies presents an average = 4 claims per policy. (i) Compute an a priory estimate of numbers of claims per policy. [2 Marks] (ii) Determine the posterior distribution of A. Give your argument. [5 Marks] (iii) Compute an a posteriori estimate of numbers of claims per policy. [3 Marks]arrow_forward
- 2. The size of a claim is modelled by F(a, λ) with a fixed a a maximum likelihood estimate of A given a sample x with a sample mean x = 11 = 121. Give [5 Marks]arrow_forwardRobbie Bearing Word Problems Angles name: Jocelyn date: 1/18 8K 2. A Delta airplane and an SouthWest airplane take off from an airport at the same time. The bearing from the airport to the Delta plane is 23° and the bearing to the SouthWest plane is 152°. Two hours later the Delta plane is 1,103 miles from the airport and the SouthWest plane is 1,156 miles from the airport. What is the distance between the two planes? What is the bearing from the Delta plane to the SouthWest plane? What is the bearing to the Delta plane from the SouthWest plane? Delta y SW Angles ThreeFourthsMe MATH 2arrow_forwardFind the derivative of the function. m(t) = -4t (6t7 - 1)6arrow_forward
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