CALCULUS:GRAPHICAL...,AP ED.-W/ACCESS
5th Edition
ISBN: 9780133314564
Author: Finney
Publisher: SAVVAS L
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Shown below are six statements about functions. Match each statement to one of the functions shown below which BEST matches that
statement.
1. limx→7+ f(x) and limx→7- f(x) both exist and are finite, but they are not equal.
2. The graph of y = f(x) has vertical tangent line at (7, ƒ(7))
3. lim 7 f(x) = -∞o.
4. limx→7+ f(x) exists but limx→7- f(x) does not.
5. limx→7 f(x) = ∞0.
6. lim→7 f(x) exists but f is not continuous at 7.
A. f(x) =
B. f(x) =
cos (¹7)
0
F. f(x) =
2x + 28
2x
0
28
(x-7)²
c. f(x) =
D. f(x)=√x-7
E. f(x) =
1
x-7
2x
0
2x
2x
if x 7
if x 7
if x 7
Suppose that f(x) = Aæ² + Bx.
Find the values of the constants A and B if f(2) = -4 and
%3D
[A(-1+h)² + B(-1+h)] – [A – B]
lim
h→0
= -6.
h
A =
(Enter an integer)
B =
(Enter an integer)
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- Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?arrow_forwardbThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.arrow_forwardIf xis large, which function grows faster, f(x)=2x or g(x)=x2?arrow_forward
- When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal stretch from a vertical stretch?arrow_forwardIn this problem you are asked to find a function that models in real life situation and then use the model to answer questions about the guidelines on page 273 to help you. Minimizing Time A man stands at a point A on the bank of a straight river, 2 mi wide. To reach point B, 7 mi downstream on the opposite bank, he first rows his boat to point Pon the opposite bank and then walks the remaining distances x to B, as shown in the figure. He can row at a speed or 2 mi/h and walk as a speed of mi/h (a) Find a function that models the time needed for the trip. (b) Where should he land so that he reaches B as soon as possible?arrow_forwardDetermine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.arrow_forward
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