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Question For this problem, consider the function on the domain of all real numbers. (a) The value of is Oo . (If you ne...
Question For this problem, consider the function y=f(x)= |x| + x 3 on the domain of...
Question For this problem, consider the function
y=f(x)=
|x|
+
x
3
on the domain of all real numbers.
(a) The value of
limx→
∞f(x)
is
. (If you need to use -∞ or ∞, enter -infinity or
infinity.)
(b) The value of
limx→
−∞f(x)
is
. (If you need to use -∞ or ∞, enter -infinity or
infinity.)
(c) There are two x-intercepts; list these in increasing
order: s=
, t=
.
(d) The intercepts in part (c) divide...
EXAMPLE 3 Sketch the graph of x) = 5xe". (A) The domain of f is R....
EXAMPLE 3 Sketch the graph of x) = 5xe". (A) The domain of f is R. (B) The x- and y-intercepts are both (C) Symmetry: None. (D) Because both 5x and ex become large as x →oo, we have limx→”5xex=00, As x →-oo, however, ex→ and so we have an indeterminate product that requires the use of l'Hospital's Rule: 5xlim Video Example Thus the x-axis is a horizontal asymptote (E) f(x) = 5xex + 5e" = Since ex is always...
Refer to the graphs in the specified exercises from Section 2.5. For each graph, determine the...
Refer to the graphs in the specified exercises from Section 2.5.
For each graph, determine the following: the domain and range (use
interval notation), the zeroes of the function (use set notation
and write the values in increasing order), the open intervals on
which the function is positive or negative (interval notation), the
open intervals on which the function is increasing and decreasing
(interval notation), and any local max or local min value(s) (write
as points separated by commas, if...
Use the guidelines to sketch the curve y = 2x^2/x^2 - 1. The domain is {x...
Use the guidelines to sketch the curve y = 2x^2/x^2 - 1. The domain is {x | x^2 - 1 0} = {x | x plusminus 1} The x- and y-intercepts are both 0. Since f(-x) = f(x), the function f is. The curve is symmetric about the y-axis. Since the denominator is 0 when x = plusminus1, we compute the following limits: Therefore the lines x = 1 and x = are vertical asymptotes. This information about limits and...
4) Identify the following key features/properties using intervals only: intervals when the function is positive/negative, intervals when the function is increasing/decreasing, intervals when t...
4) Identify the following key features/properties using intervals only: intervals when the function is positive/negative, intervals when the function is increasing/decreasing, intervals when the slope of the function is positive/negative, and intervals when the slope of the function is increasing/decreasing do the questions.) All calculations must be performed using exact values (fractions and radicals) cm Part A - Knowledge/Understanding and Application, Making Connections 1) Sketch the rational function f(x) hand: domain, intercepts, asymptotes, and behavior near the asymptotes. You would...
The graph of a rational function fis shown below. Assume that all asymptotes and intercepts are...
The graph of a rational function fis shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes". Use the graph to complete the following. (a) Find all x-intercepts and y-intercepts. Check all that apply. X-intercept(s): 4 00 01 None . : O=D y-intercept(s): 01 04 00 None Dando None (0,0) HHH [0,0] (0,0] [0,0) (b) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary....
f(T) = 22 9 Instructions: • If you are asked for a function, enter a function....
f(T) = 22 9 Instructions: • If you are asked for a function, enter a function. • If you are asked to find 2- or y-values, enter either a number or a list of numbers separated by commas. If there are no solutions, enter None. • If you are asked to find an interval or union of intervals, use interval notation. Enter { } if an interval is empty • If you are asked to find a limit, enter either...
Using interval notation, determine the largest domain over which the given function is one-to-one. Then, provide...
Using interval notation, determine the largest domain over which the given function is one-to-one. Then, provide the equation for the inverse of the function that is restricted to that domain. If two equally large domains exist over which the given function is one-to-one, you may use either domain. However, be certain that the equation for the inverse function you submit is appropriate for the particular domain you choose. f(x) = x² + 18x (Give your answer as an interval in...
im having trouble understanding limits (1) Use the given graph of the function f(x) to answer...
im having trouble understanding limits
(1) Use the given graph of the function f(x) to answer the following questions. 3 2 0 0 -1 -2 Find the limit of f(x) as x -+0+ for ” does not exist” enter ” DNE” 79 79 99 for enter negative in finity” for ” +00” enter " positive in finity" (1) Use the given graph of the function f(x) to answer the following questions. 3 2 0 0 1 2 3 4 -27...
The graph of a rational function f is shown below. Assume that all asymptotes and intercepts...
The graph of a rational function f is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes", Use the graph to complete the following. (a) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary. Select "None" as necessary. : None O=o (0,0) Dando Vertical asymptote(s): 1 Horizontal asymptote(s): U [0,0] (0,0) (0,0) O ovo 00 - - -8 EEE-- - -6 1 (b)...
Question For this problem, consider the function
y=f(x)=
|x|
+
x
3
on the domain of all real numbers.
(a) The value of
limx→
∞f(x)
is
. (If you need to use -∞ or ∞, enter -infinity or
infinity.)
(b) The value of
limx→
−∞f(x)
is
. (If you need to use -∞ or ∞, enter -infinity or
infinity.)
(c) There are two x-intercepts; list these in increasing
order: s=
, t=
.
(d) The intercepts in part (c) divide...
EXAMPLE 3 Sketch the graph of x) = 5xe". (A) The domain of f is R. (B) The x- and y-intercepts are both (C) Symmetry: None. (D) Because both 5x and ex become large as x →oo, we have limx→”5xex=00, As x →-oo, however, ex→ and so we have an indeterminate product that requires the use of l'Hospital's Rule: 5xlim Video Example Thus the x-axis is a horizontal asymptote (E) f(x) = 5xex + 5e" = Since ex is always...
Refer to the graphs in the specified exercises from Section 2.5.
For each graph, determine the following: the domain and range (use
interval notation), the zeroes of the function (use set notation
and write the values in increasing order), the open intervals on
which the function is positive or negative (interval notation), the
open intervals on which the function is increasing and decreasing
(interval notation), and any local max or local min value(s) (write
as points separated by commas, if...
Use the guidelines to sketch the curve y = 2x^2/x^2 - 1. The domain is {x | x^2 - 1 0} = {x | x plusminus 1} The x- and y-intercepts are both 0. Since f(-x) = f(x), the function f is. The curve is symmetric about the y-axis. Since the denominator is 0 when x = plusminus1, we compute the following limits: Therefore the lines x = 1 and x = are vertical asymptotes. This information about limits and...
4) Identify the following key features/properties using intervals only: intervals when the function is positive/negative, intervals when the function is increasing/decreasing, intervals when the slope of the function is positive/negative, and intervals when the slope of the function is increasing/decreasing do the questions.) All calculations must be performed using exact values (fractions and radicals) cm Part A - Knowledge/Understanding and Application, Making Connections 1) Sketch the rational function f(x) hand: domain, intercepts, asymptotes, and behavior near the asymptotes. You would...
The graph of a rational function fis shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes". Use the graph to complete the following. (a) Find all x-intercepts and y-intercepts. Check all that apply. X-intercept(s): 4 00 01 None . : O=D y-intercept(s): 01 04 00 None Dando None (0,0) HHH [0,0] (0,0] [0,0) (b) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary....
f(T) = 22 9 Instructions: • If you are asked for a function, enter a function. • If you are asked to find 2- or y-values, enter either a number or a list of numbers separated by commas. If there are no solutions, enter None. • If you are asked to find an interval or union of intervals, use interval notation. Enter { } if an interval is empty • If you are asked to find a limit, enter either...
Using interval notation, determine the largest domain over which the given function is one-to-one. Then, provide the equation for the inverse of the function that is restricted to that domain. If two equally large domains exist over which the given function is one-to-one, you may use either domain. However, be certain that the equation for the inverse function you submit is appropriate for the particular domain you choose. f(x) = x² + 18x (Give your answer as an interval in...
im having trouble understanding limits
(1) Use the given graph of the function f(x) to answer the following questions. 3 2 0 0 -1 -2 Find the limit of f(x) as x -+0+ for ” does not exist” enter ” DNE” 79 79 99 for enter negative in finity” for ” +00” enter " positive in finity" (1) Use the given graph of the function f(x) to answer the following questions. 3 2 0 0 1 2 3 4 -27...
The graph of a rational function f is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes", Use the graph to complete the following. (a) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary. Select "None" as necessary. : None O=o (0,0) Dando Vertical asymptote(s): 1 Horizontal asymptote(s): U [0,0] (0,0) (0,0) O ovo 00 - - -8 EEE-- - -6 1 (b)...
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