NYU 6 The Definite Integral Exam Practice The first photo is the instructions. I need answer in PDF. Take this task only u good at calculus and these questions are easy to u You must be in Classic mode for the two screen shots so nothing scrolls off the screen. Do all six problems at

4 points.

5.4 Applications #2 You must use calculus (not completing the square) and show the critical point is a

maximum. State your answer in English

5.5 Indeterminate #4

6.1 Tangents, Differential Choose #10 or #38

6.2 Newton #8 Put in a screen shot like Figure 2. You may need to scroll up to show the first line. The press

ENTER two more times so the answers agree well.

6.4 Trigonometry #12

7.2 Definite integral #10. You must paste in a screen shot like figure 2, but also in you check with fnlnt.

= 90 ,

lile giu. Dingol110-114″ > 108″, so the postal clerk says the

121)

package is oversize and you must pay triple. No you say and increase the height to 25″,

es per acre. How many trees

40, yield decreases by (a) ;

is y = 253 if 0 < x < 40 and
5
Practice 3
2. Rewrite A =
?
+
b> 3(2ar2.

2. Because y’ < 0 if I < 45
lute maximum.
= 55 Because y'>0 if

gives the absolute maximum.

which is now the length. The girth is now ad = 24 = 75.4.

Length + girth = 25 + 75.4 = 100.4″ < 108". In 2005 the USPS solved this problem by
defining 7 = 4 (perimeter of enclosing rectangle) so
girth is 4 x 24 = 96". Problem 16 asks
you to find the maximum volume under the old rules.
Practice Answers 1. Yes, f(2) is the absolute maximum
on (0,5 ]; the maximum on a subset (0.4) cannot be larger.
2??2 +
22.100.100)1/3 = 3(200004)1/3 = 119.27in with
equality when 25r2 = 100, ,3 = 50, r = (59)1/3
.
3. Y1=25X(X 40) See the figure.
4. x is in closed interval (-1,1]; test the end points.
h
Problems 5.4 Labels and " denote hint and note below; & denotes solution in the Student's Solutions Manual.
Remember to test the critical point and state the answer in English with units.
Problems 1-14 deal with plane geometry.
1h Suppose that 240 feet of fencing will be used to enclose a rectangular field. Find the dimensions of the
rectangle that will yield the largest possible area.
2" Sam wants to build a rectangular enclosure to display shrubs. Three sides will be built from chain-link fence
costing $20 per running foot, and the remaining side will be built from cedar fence costing $10 per running
xample 7b on a TI-83 in a
(3)
the graph.
+9+z4,
3)
ad f'>0 if x > 1. Hence = 1,

foot. Find the dimensions of the enclosure of largest possible area that can be built with $2000 worth of fence.

In Problemos 3-4, a rectangular enclosure is formed by using all or part of a 100 foot wall. Objective is piecewise.

gho Find the maximum area if the amount f of fencing used is 120 ft.

4″ Find the maximum area if the amount f of fencing used is (b) 240 ft (c) 360ft.

5h An agriculturalist wants to enclose

t at (1,1).

ncing parallel to two of

Hospital’s rule

732/3 5,1/3

2

7 – 5/21/3 + 2/2213

en 2. lim

. 72213

–

= lim

422/3 +62

+6×1/3 – 3 1/22/3 4+6//3 – 3/2273

roblems with “have hints below; those with have solutions in

17, state the type and find the limit. In Problem 9, the variable

1 1

2)

4×3 – 5x +1

4. lim

x1

In x

2.

1° lim Inx

x-13 – 1

59

8

al SULUI

VIUIL

3

1* f(t) = x2 3x + 4 at (1, 2); x = 0.97

3. y=(x+1/2)(x2 1) at x = 1; x = 1.06

e

)

2

58 f(x)=

x+ +1

2

2. f(x) = x2 + 2 at (1,3); t = -1.04

4. y = (3×2 + 7)(x + 2) at (-1,10); 2 = -0.92

22 4 at x = -2; x = -2.03

5

6. Y=

at x = –

= -3; x = -3.2

V x2 +16

7. f(x) = V x2 +9 at (4,5); x = 4.1

8. f(x) = xV x2 – 16 at 2 = 5; x = 4.9

g* f(2)=(3-2) at x = 2; x = 1.95

10. The relative signal frequency due to operation at the fraction r of light speed is f(2)= (1+2)/(1-2).

Galactic Tours operates at close to 60% of light speed. Find a linear approximation to f. Estimate the

relative frequency when operating at 63%.

11′ Let y = 223 3×2 – 12x + 5. Find the points on the graph where the tangent line is horizontal.

12. Find the equation of the tangent line to y = ln(3x + 2) having slope 1.

ls” Find the point on the graph of y = 222 – 3x + 4 where the slope of the tangent line is 9. Write the equation.

14. Each given graph has one point P such that the tangent at P passes through (0,0). Find the coordinates of P.

Be sure to simplify the y-coordinate. (a) y = 1.5″ (b) y = .7″ (C) y = at

15. Find the poi

rough the origin.

5.

(b) How long will it take the population UU ITUCII UJU!

(c) What will the population be after many years?

6. A cancer treatment facility has 5000 patients. Each year 15% die and 200 are considered cured and released;

d

no new patients are accepted.

(a) How many patients are left after 3 years?

(b) When will the facility be able to close?

6

in Problems 710, use Newton’s method to find a root of the equation to at least 6 decimal places.

16

7. 6x² 8×3+1=0

8. x3 + x – 3=0

gº z + In r = 3

10. et +1 = x2

11. The cost function for a certain manufacturer is c(x) = 400 + 2x +0.123/2. Use Newton’s method to estimate

how many items can be produced for $1000. Start with x = 100.

12. Find the volume of 1 mole of O, at 415K and 310 bar by solving the van der Waals’ equation

310 – 08314 x 415 1.382

Start at the ideal

.08314 x 415

value

gas

v2

310

= .1L

V-.0319

13. The dose dug required to treat a spherical tumor of radius r mm depends on the surface area and volume V

according to the formula d = 0.25 +0.3V = 0.2.41r+0.3 APO = 0.872 +0.47r. What size tumor requires

a dose of 50

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