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Ap Calculus Bc

Class 12 Ap Calculus Bc Questions asked by Filo students

Views: 5,691

f (x) = x + 2 - x

g (u) = u + 2 - u,

is it true that

f = g ?

Topic:

AP Calculus BC

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Views: 5,390

The graph of a function

f

is given.(a) State the value of

f (1) .

(b) Estimate the value of

f (- 1)

(c) For what values of

x

f (x) = 1 ?

(d) Estimate the value of

x

f (x) = 0

(e) State the domain and range of

f

(f) On what interval is

f

Topic:

AP Calculus BC

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Views: 5,797

f

g

are given.(a) State the values of

f (- 4)

g (3)

(b) For what values of

x

f (x) = g (x)?

(c) Estimate the solution of the equation

f (x) = - 1

(d) On what interval is

f

decreasing?(e) State the domain and range of

f

(f) State the domain and range of

g .

Topic:

AP Calculus BC

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Views: 5,900

7 - 10

Determine whether the curve is the graph of a function of

x .

If it is, state the domain and range of the function.

Topic:

AP Calculus BC

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Views: 5,039

Temperature readings

T

^{\circ} F

) were recorded every two hours from midnight to

2 : 00 PM

in Phoenix on September

10, 2008

t

was measured in hours from midnight.

t T 082275474675884109012931494

(a) Use the readings to sketch a rough graph of

T

as a function of

t

.(b) Use your graph to estimate the temperature at

9 : 00

Topic:

AP Calculus BC

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Views: 5,225

31 - 37

Find the domain of the function.

g (t) = 3 - t - 2 + t

Topic:

AP Calculus BC

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Views: 5,829

39 - 50

Find the domain and sketch the graph of the function.

f (x) = {3 - \frac{1}{2} x 2 x - 5 if x ⩽ 2 if x > 2

Topic:

AP Calculus BC

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Views: 5,222

39 - 50

Find the domain and sketch the graph of the function.

f (x) = {x + 2 x^{2} if x ⩽ - 1 if x > - 1

Topic:

AP Calculus BC

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Views: 5,388

39 - 50

Find the domain and sketch the graph of the function.

f (x) = {x + 9 if x 3

Topic:

AP Calculus BC

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Question 10

Views: 5,073

\begin{equation}\begin{array}{l}{57-61 \text { Find a formula for the described function and state its }} \\ {\text { domain. }}\end{array}\end{equation}An open rectangular box with volume 2

m^{3}

has a square base. Express the surface area of the box as a function of the length of a side of the base.

Topic:

AP Calculus BC

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Question 11

Views: 5,078

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side

x

at each corner and then folding up the sides as in the figure. Express the volume

V

of the box as a function of

X .

Topic:

AP Calculus BC

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Question 12

Views: 5,624

In a certain country, income tax is assessed as follows. There is no tax on income up to 10,000 .

A n y in co m eo v er

10, 000

is taxed at a rate of

10%,

up to an income of 20,000 .

A n y in co m eo v er

20, 000

%.

(a) Sketch the graph of the tax rate

R

as a function of the income I.(b) How much tax is assessed on an income of \\\ 14,000 ?

O n

26, 000 ?

(c) Sketch the graph of the total assessed tax

T

as a function of the income I.

Topic:

AP Calculus BC

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Question 13

Views: 5,577

f

[- 5, 5]

and a portion of its graph is shown.(a) Complete the graph of

f

if it is known that

f

is even.(b) Complete the graph of

f

if it is known that

f

Topic:

AP Calculus BC

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Question 14

Views: 5,958

73 - 78

Determine whether

f

is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually.

f (x) = 1 + 3 x^{2} - x^{4}

Topic:

AP Calculus BC

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Question 15

Views: 5,207

Jason leaves Detroit at

2 : 00 PM

and drives at a constant speedwest along

1 - 96.

He passes Ann Arbor, 40

mi

from Detroit, at

2 : 50 PM

(a) Express the distance traveled in terms of the time elapsed.(b) Draw the graph of the equation in part (a).(c) What is the slope of this line? What does it represent?

Topic:

AP Calculus BC

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Question 16

Views: 5,147

Biologists have noticed that the chirping rate of crickets of acertain species is related to temperature, and the relationshipappears to be very nearly linear. A cricket produces 113 chirpsper minute at

7 0^{\circ} F

and 173 chirps per minute at

8 0^{\circ} F

(a) Find a linear equation that models the temperature Tas a function of the number of chirps per minute N . (b) What is the slope of the graph? What does it represent? (c) If the crickets are chirping at 150 chirps per minute, estimate the temperature.

Topic:

AP Calculus BC

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Question 17

Views: 5,402

The table shows (lifetime) peptic ulcer rates (per 100 popu-lation) for various family incomes as reported by the NationalHealth Interview Survey.\begin{array}{l}{\text { (a) Make a scatter plot of these data and decide whether a }} \\ {\text { linear model is appropriate. }} \\ {\text { (b) Find and graph a linear model using the first and last data }} \\ {\text { points. }} \\ {\text { (c) Find and graph the least squares regression line. }} \\ {\text { (d) Use the linear model in part (c) to estimate the ulcer rate }} \\ {\text { for an income of } \ 25,000 .}\end{array}\begin{array}{l}{\text { (e) According to the model, how likely is someone with an }} \\ {\text { income of } \ 80,000 \text { to suffer from peptic ulcers? }} \\ {\text { (f) Do you think it would be reasonable to apply the model to }} \\ {\text { someone with an income of } \ 200,000 ?}\end{array}

Topic:

AP Calculus BC

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Question 18

Views: 5,150

Biologists have observed that the chirping rate of crickets of acertain species appears to be related to temperature. The tableshows the chirping rates for various temperatures.

(a) Make a scatter plot of the data. (b) Find and graph the regression line. (c) Use the linear model in part (b) to estimate the chirping rate at 10 0^{\circ} F .

Topic:

AP Calculus BC

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Question 19

Views: 5,368

It makes sense that the larger the area of a region, the larger the number of species that inhabit the region. Many ecologists have modeled the species-area relation with a power function and, in particular, the number of species

S

of bats living in caves in central Mexico has been related to the surface area

A

of the caves by the equation

S = 0.7 A^{0. 3} .

(a) The cave called Mision Imposible near Puebla, Mexico, has a surface area of A = 60 m^{2} . How many species of bats would you expect to find in that cave? (b) If you discover that four species of bats live in a cave, estimate the area of the cave.

Topic:

AP Calculus BC

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Question 20

Views: 5,051

The table shows the mean (average) distances

d

of the planets from the sun (taking the unit of measurement to be the distance from the earth to the sun) and their periods

T

(time of revolution in years).

(a) Fit a power model to the data. (b) Kepler’s Third Law of Planetary Motion states that "The square of the period of revolution of a planet is proportional to the cube of its mean distance from the sun." Does your model corroborate Kepler’s Third Law?

Topic:

AP Calculus BC

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