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Question: A machinist is required to manufacture a


A machinist is required to manufacture a circular metal disk with area 1000cm2.
(a). What radius produces such a disk?
(b). If the machinist is allowed an error tolerance of ±5 cm2 in the area of the disk, how close to the ideal radius in part (a) must the machinist control the radius?
(c). In terms of ∈1δ the definition of limx→a f (x) = L, what is x? What is f (x)? What is a? What is L? What value of ∈ is given? What is the corresponding value of δ?


> Radiation and chemotherapy drugs preferentially kill cells that divide frequently, most notably cancer cells. These cancer treatments also cause hair to fall out. Why?

> _______ in arteries sense changes in the acidity of the blood. a. Mechanoreceptors b. Neurotransmitters c. Photoreceptors d. Chemoreceptors

> Most oxygen transported in blood ________. a. is bound to hemoglobin b. combines with carbon to form carbon dioxide c. is in the form of bicarbonate d. is dissolved in the plasma

> When you breathe quietly, inhalation is and exhalation is ________. a. passive; passive b. active; active c. passive; active d. active; passive

> Increased industrialization in China has environmentalists worried about air quality elsewhere. Are air pollutants emitted in Beijing more likely to end up in eastern Europe or the western United States? Why?

> Which holds the most dissolved oxygen? a. warm, still water b. warm, running water c. cold, running water d. cold, still water

> In human lungs, gas exchange occurs at the ______. a. bronchi b. bronchioles c. alveoli d. pleural sacs

> The tracheal tubes of insects carry ______ to tissues deep inside the body. a. hemolymph b. blood c. air d. water

> In a, air flows continually across the respiratory surface. a. fish b. bird c. frog d. mammal

> A developing fetus obtains oxygen from its mother’s blood. In an organ called the placenta, fetal capillaries run through and exchange substances with maternal blood. The hemoglobin made by a fetus has different properties than that made after birth. At

> 1. Respiratory proteins such as hemoglobin ________. a. contain metal ions b. occur only in vertebrates c. increase the efficiency of oxygen transport d. both a and c 2. _____ binds to hemoglobin even more strongly than oxygen does. a. Carbon dioxide b.

> The red blood cell enzyme carbonic anhydrase contains a zinc cofactor. A diet deficient in zinc does not reduce the number of red blood cells, but it impairs respiratory function by reducing CO2 output. Explain why.

> _____tissues are sheetlike with one free surface. a. Epithelial b. Muscle c. Nervous d. Connective

> IPSCs are nearly identical to human embryonic stem cells in terms of gene expression, but there may be other ways in which they are not equivalent. For example, the telomeres of IPSCs often vary in length, with many IPSCs cells having telomeres shorter t

> In 1798, a stuffed platypus specimen was delivered to the British Museum. Reports that it laid eggs created much confusion. To modern biologists, a platypus is clearly a mammal. It has fur and the females produce milk. Young animals have typical mammalia

> London, England, is at the same latitude as Calgary in Canada’s province of Alberta. However, the mean January temperature in London is 5.5°C (42°F), whereas in Calgary it is minus 10°C (14°F). Compare the locations of these two cities and suggest a reas

> Tree rings occur ______. a. when there are droughts during the time the rings form b. where environmental conditions influence xylem cell size c. if heartwood alternates with sapwood d. as epidermis replaces periderm

> The activity of lateral meristems ______ older roots and stems. a. lengthens b. thickens c. both a and b

> Root hairs ______. a. conduct water from cortex to aboveground shoots b. increase the root’s surface area for absorption c. anchor the plant in soil

> A dendritic cell engulfs a bacterium, then presents bacterial bits on its surface along with a(n) ________. a. MHC marker b. antibody c. T cell receptor d. antigen

> Antibodies are ______. a. antigen receptors b. made only by B cells c. proteins d. all of the above

> ____  trigger(s) immune responses. a. Cytokines b. Lysozyme c. Antibodies d. Antigens e. Histamines f. MHC markers

> A flu shot is a vaccine for several strains of influenza virus. This year, you get the shot and “the flu.” What happened? (There are at least three explanations.)

> Which artery carries oxygen-poor blood?

> Which of the following has the thickest wall? a. left atrium b. left ventricle c. right atrium d. right ventricle

> Blood pressure is highest in the and lowest in the _________. a. arteries; veins b. arterioles; venules c. veins; arteries d. capillaries; arterioles

> Match the terms with the most suitable description. a. broadleaf forest near equator b.partly enclosed by land; where tundra chaparral desert fresh water and seawater mix c. African grassland with trees d.low-growing plants at high latitudes or eleva

> Blood flows directly from the left atrium to ___________. a. the aorta b. the left ventricle c. the right atrium d. the pulmonary arteries

> The plasma protein albumin is made by ______. a. white blood cells b. red blood cells c. the heart d. the liver

> 1. In ________ blood flows through two completely separate circuits. a. birds b. mammals c. fish d. both a and b 2. The _______ circuit carries blood to and from lungs. a. systemic b. pulmonary 3. Platelets function in ______. a. oxygen transport b. bl

> In a(n) _______, the primary root is typically the largest. a. lateral meristem b. adventitious root system c. fibrous root system d. taproot system

> Is an onion a root or a stem?

> Typically, vascular tissue is organized as in stems and as in roots. a. multiple vascular bundles; one vascular cylinder b. one vascular bundle; multiple vascular cylinders c. one vascular cylinder; multiple vascular bundles d. multiple vascular cylinder

> A vascular bundle in a leaf is called ______. a. a vascular cylinder b. mesophyll c. a vein d. vascular cambium

> Epidermis and periderm are ______ tissues. a. ground b. vascular c. dermal

> All of the vascular bundles inside a typical ______ are arranged in a ring. a. monocot stem b. eudicot stem c. monocot root d. eudicot root

> Which of these traits are retained by an adult lancelet?

> Individuals help sustain biodiversity by ___________. a. reducing consumption b. reusing materials c. recycling materials d. all of the above

> True or false? Most species that evolved have already become extinct.

> Find the points on the given curve where the tangent line is horizontal or vertical. r=1- sine

> Find the points on the given curve where the tangent line is horizontal or vertical.  

> Find the points on the given curve where the tangent line is horizontal or vertical. r= e°

> Find the points on the given curve where the tangent line is horizontal or vertical. r= 3 cos e 3 cos

> Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. r= cos(0/3), e= T

> Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. r= cos 20, e = T/4

> Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. r%3D 2 — sin 6, ө— п/3

> Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. r= 1/6, 0 = T

> Evaluate ∑ni-1 3/2i-1.

> Prove the formula for the sum of a finite geometric series with first term and common ratio r ≠ 1: a(r* – 1) E ari- = a + ar + ar? + · .. + ar"-1 %3D i-1 r- 1

> Show that the curve r = sin θ tan θ (called a cissoid of Diocles) has the line x = 1 as a vertical asymptote. Show also that the curve lies entirely within the vertical strip 0 < x < 1. Use these facts to help sketch the cissoid.

> Show that the polar curve r = 4 + 2 sec θ (called a conchoid) has the line x = 2 as a vertical asymptote by showing that limr→±∞ x = 2. Use this fact to help sketch the conchoid.

> The figure shows a graph of r as a function of &Icirc;&cedil; in Cartesian coordinates. Use it to sketch the corresponding polar curve. TA 2- -2-

> The figure shows a graph of r as a function of &Icirc;&cedil; in Cartesian coordinates. Use it to sketch the corresponding polar curve. TA 2+ 1-

> Sketch the curve with the given polar equation. r = 1 + 2 cos (θ/2)

> Sketch the curve with the given polar equation. r = 1 + 2 cos 2θ

> Use a calculator to find the length of the curve correct to four decimal places. r = 4 sin 30

> Use a calculator to find the length of the curve correct to four decimal places. r= 3 sin 20

> Find the exact length of the polar curve. r = θ, o < θ < 2π

> Find the exact length of the polar curve. r = θ2, o < θ < 2π

> Sketch the curve and find the area that it encloses. r = 2 – sin θ

> Find the exact length of the polar curve. r = e2θ, o < θ < 2π

> Find the exact length of the polar curve. r = 3 sin θ, o < θ < π/3

> Use a graph to estimate the values of θ for which the curves r = 3 + sin 5θ and r = 6 sin θ intersect. Then estimate the area that lies inside both curves.

> Sketch the curve with the given polar equation. r = 2 cos 4θ

> Find all points of intersection of the given curves. r2 = sin 2θ, r2 = cos 2θ

> Find all points of intersection of the given curves. r = sin θ, r = 2θ

> Find all points of intersection of the given curves. r = cos 3θ, r = 3θ

> Find all points of intersection of the given curves. r = 2 sin 2θ, r = 1

> Sketch the curve with the given polar equation. r = 1 – 3 cos θ

> Sketch the curve with the given polar equation. r = 2 (1- sin θ), θ > 0

> Evaluate the integral. f x – 9/(x + 5) (x – 2), dx

> Sketch the curve with the given polar equation. r = -3 cos θ

> Find the area of the region that lies inside both curves. r= sin 20, r = cos 20

> Find the area of the region that lies inside both curves. r = 1+ cos 0, r=1- cos e %3D

> Find the area of the region that lies inside both curves. r= V3 cos 0, r= sin e

> If u (x) = f (x) + ig (x) is a complex-valued function of a real variable x and the real and imaginary parts f (x) and g (x) are differentiable functions of x, then the derivative of u is defined to be u'(x) = f'(x) + ig'(x). Use this together with Equat

> Find the area of the region that lies inside the first curve and outside the second curve. r= 3 sin 0, r= 2 - sin e

> Use Euler&acirc;&#128;&#153;s formula to prove the following formulas for cos x and sin x: eir + e-ir cos x eir – e-ir sin x 2 2i

> Use De Moivre’s Theorem with n = 3 to express cos 3θ and sin 3θ in terms of cos θ and sin θ.

> Write the number in the form a + bi. e π+i

> Write the number in the form a + bi. e 2 + iπ

> Write the number in the form a + bi. e -iπ

> Write the number in the form a + bi. e iπ/3

> Write the number in the form a + bi. e 2πi

> Write the number in the form a + bi. e iπ/2

> Find the indicated roots. Sketch the roots in the complex plane. The cube roots of 1 + i

> Find the indicated roots. Sketch the roots in the complex plane. The cube roots of i

> Find the area of the region that lies inside the first curve and outside the second curve. r= 3 cos 0, r=1+ cos e

> Find the indicated roots. Sketch the roots in the complex plane. The fifth roots of 32

> Find the indicated roots. Sketch the roots in the complex plane. The eighth roots of 1

> Find the indicated power using De Moivre’s Theorem. (1 – i)8

> Find the indicated power using De Moivre’s Theorem. (2√3 + 2 i)5

> Find the indicated power using De Moivre’s Theorem. (1 – √3 i)5

> Find the indicated power using De Moivre’s Theorem. (1 + i)20

> Find polar forms for zw, z/w, and 1/z by first putting z and w into polar form. = 4(/3 + i), w = -3 – 3i

> Find polar forms for zw, z/w, and 1/z by first putting z and w into polar form. z = 2/3 – 2i, w = -1 +i

> Find polar forms for zw, z/w, and 1/z by first putting z and w into polar form. z = 4/3 – 4i, w = 8i %3D %3D

> Find polar forms for zw, z/w, and 1/z by first putting z and w into polar form. z = 3 + i, w = 1 + v3i

> Find the area of the region that lies inside the first curve and outside the second curve. r=1- sin 6, r= 1

> Write the number in polar form with argument between 0 and 2π. 8i

2.99

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