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Calculus
for the function (x+1)/(x^(2)-1)
(a) Determine all local maxima, minima and all inflection points with their function values.
(b) Are there any vertical asymptotes? Determine the behaviour of f as x approaches infinity and x approaches negative infinity
(c) Determine the x- and the y-intercepts.
(a) Determine all local maxima, minima and all inflection points with their function values.
(b) Are there any vertical asymptotes? Determine the behaviour of f as x approaches infinity and x approaches negative infinity
(c) Determine the x- and the y-intercepts.
Calculus
for the function (x+1)/(x^(2)-1)
(a) Determine all candidates c 2 D for inflection points, i.e. those c E D for which f''(c) does not exists or for which f''(c) = 0.
(b) On which intervals is f increasing and on which ones is it decreasing?
(c) On which intervals is f concave up and on which ones is it concave down?
(a) Determine all candidates c 2 D for inflection points, i.e. those c E D for which f''(c) does not exists or for which f''(c) = 0.
(b) On which intervals is f increasing and on which ones is it decreasing?
(c) On which intervals is f concave up and on which ones is it concave down?
Calculus
for the function (x+1)/(x^(2)-1)
(a) Determine the domain D of f.
(b) Is the function even (i.e. f(-x) = f(x) for all x), is it odd (i.e. f(-x) = -f(x) for all x) or neither?
(c) Determine all critical points of f.
(a) Determine the domain D of f.
(b) Is the function even (i.e. f(-x) = f(x) for all x), is it odd (i.e. f(-x) = -f(x) for all x) or neither?
(c) Determine all critical points of f.
Calculus
Let f(x)=(x^2)/((x−5)^2). Answer the following questions. 1. Find the vertical asymptote(s) of f. Answer (separate by commas): x=?? 2. Find the horizontal asymptote(s) of f. Answer (separate by commas): y=? 3. Find the interval(s) on which f is increasing. Answer (in interval notation):? 4. Find the interval(s) on which f is decreasing. Answer (in interval notation):?
Calculus
Find the derivative of y=x-4 and name the rules that you used.
4x+7x^2 all divided by x, find the derivative.
Find the values of x for y=-5x^2-2x
4x+7x^2 all divided by x, find the derivative.
Find the values of x for y=-5x^2-2x
Calculus
Let f(x)=(x^2)/((x−5)^2). Answer the following questions. 1. Find the vertical asymptote(s) of f.
Answer (separate by commas): x=
2. Find the horizontal asymptote(s) of f.
Answer (separate by commas): y=
3. Find the interval(s) on which f is increasing.
Answer (in interval notation):
4. Find the interval(s) on which f is decreasing.
Answer (in interval notation):
5. Find the local maxima of f. List your answers as points in the form (a,b).
Answer (separate by commas):
6. Find the local minima of f. List your answers as points in the form (a,b).
Answer (separate by commas):
7. Find the interval(s) on which f is concave upward.
Answer (in interval notation):
8. Find the interval(s) on which f is concave downward.
Answer (in interval notation):
Answer (separate by commas): x=
2. Find the horizontal asymptote(s) of f.
Answer (separate by commas): y=
3. Find the interval(s) on which f is increasing.
Answer (in interval notation):
4. Find the interval(s) on which f is decreasing.
Answer (in interval notation):
5. Find the local maxima of f. List your answers as points in the form (a,b).
Answer (separate by commas):
6. Find the local minima of f. List your answers as points in the form (a,b).
Answer (separate by commas):
7. Find the interval(s) on which f is concave upward.
Answer (in interval notation):
8. Find the interval(s) on which f is concave downward.
Answer (in interval notation):
Calculus
For what values of the numbers a and b does the function f(x)=axe^(bx^2) have the maximum value f(3)=6.
Answer: a=
and b=
Answer: a=
and b=
Calculus
Answer the following questions for the function
f(x)=(x^(3))/(x^(2)−1)
defined on the interval [−20,16].
a.) Enter the x-coordinates of the vertical asymptotes of f(x) as a comma-separated list. That is, if there is just one value, give it; if there are more than one, enter them seperated commas; and if there are none, enter NONE .
Answer:
b.) f(x) is concave up on the region .
c.) Enter the x-coordinates of the inflection point(s) for this function as a comma-separated list.
f(x)=(x^(3))/(x^(2)−1)
defined on the interval [−20,16].
a.) Enter the x-coordinates of the vertical asymptotes of f(x) as a comma-separated list. That is, if there is just one value, give it; if there are more than one, enter them seperated commas; and if there are none, enter NONE .
Answer:
b.) f(x) is concave up on the region .
c.) Enter the x-coordinates of the inflection point(s) for this function as a comma-separated list.
Calculus
Answer the following questions for the function
f(x)=x√(x^(2)+25)
defined on the interval [−5,7].
a.) f(x) is concave down on the interval .
b.) f(x) is concave up on the interval .
c.) The minimum for this function occurs at x= .
d.) The maximum for this function occurs at x= .
f(x)=x√(x^(2)+25)
defined on the interval [−5,7].
a.) f(x) is concave down on the interval .
b.) f(x) is concave up on the interval .
c.) The minimum for this function occurs at x= .
d.) The maximum for this function occurs at x= .
Calculus
Consider the function f(x)=x^2e^(5x). For this function there are three important intervals: (−∞,A], [A,B], and [B,∞) where A and B are the critical numbers. Find A and B.
A=
B=
For each of the following intervals, tell whether f(x) is increasing (enter INC ) or decreasing (enter DEC ).
(−∞,A]:
[A,B]:
[B,∞)
A=
B=
For each of the following intervals, tell whether f(x) is increasing (enter INC ) or decreasing (enter DEC ).
(−∞,A]:
[A,B]:
[B,∞)
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#339914 on Dec 2023
#339914 on Dec 2023