Homework Answers
INTERMEDIATE VALUE THEOREM:
Continuous image of connected set is connected.
Or,
Let X and Y be two topological space. Let f:X---->Y be continuous onto map. If X is connected then f(X)=Y is also connected.
(A).
In case, range R is given trivial topology then intermediate value theorem holds good. As every subset of trivial topological space is CONNECTED.
(B).
In case, range R is given discrete topology then intermediate value theorem does NOT hold good as every two point set in discrete topological space is DISCONNECTED.
(C).
In case, range R is given lower limit topology then intermediate value theorem holds good as every subset of topological space is CONNECTED.
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#4 Determine whether the given value is from a discrete or continuous data set When a...
#4
Determine whether the given value is from a discrete or continuous data set When a limo is randomly selected, it is found to have enough room to seat 2 people. Choose the correct answer below O A. It is from a continuous data set because the number of possible values is infinite and not countable O B. tt is from a continuous data set because the number of possible values is infinite and countable ° C. It is from...
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Determine whether the Mean Value Theorem can be applied to f on the closed interval (a, b). (Select all that apply.) f(x) = 16 - xl, [3, 7] Yes, the Mean Value Theorem can be applied. No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). None of the above. If the Mean Value Theorem can be applied, find all values of c in the open...
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(4) Using the intermediate value theorem, determine, if possible, whether the function f has at least one real zero between aandb. f(x)= 3x2 - 2x -11;a=2,6 = 3 (b) Graph the polynomial (a)P(x) = 2(x + 2)(x - 1)(x – 3)
Question 2: A More detailed version of the Theorem 1 at page 24 of the textbook, called Picard's Theorem, says that If the function f(x, y) is continuous in a rectangle near the point (a, b), then at least one solution of the differential equation y' = f(x,y) exists on some open interval I containing the point If, in addition, the partial derivative is also continuous in that rectangle near (a, b), then this solution is unique on some (perhaps...
Determine whether the Mean Value Theorem can be applied to fon the closed interval (a, b). (Select all that apply.) RX) - 17 - xl. 14,8) Yes, the Mean Value Theorem can be applied. No, because fis not continuous on the closed interval [a, b]. No, because is not differentiable in the open interval (a, b). None of the above. (Ь) - Ka) ba If the Mean Value Theorem can be applied, find all values of c in the open...
7. a. Determine whether the Mean Value Theorem applies to the function f(x) = 7 - x? on the interval (-1,2) b. If so, find the point(s) that are guaranteed to exist by the Mean Value Theorem. a. Choose the correct answer below. O A. Yes, because the function is continuous on the interval [-1.2] and differentiable on the interval (-1.2). O B. No, because the function is differentiable on the interval (-1.2), but is not continuous on the interval...
need value of C
1/2 POINTS PREVIOUS ANSWERS LARCALCET7 4.R.017. Determine whether the Mean Value Theorem can be applied to fon the closed interval MY NOTES ASK YOUR TEACHER bl. (Select all that apply.) R(x) x - cos(x). Yes, the Mean Value Theorem can be applied. No, because fis not continuous on the closed interval (a, b). No, because fis not differentiable in the open interval (a, b). None of the above. If the Mean Value Theorem can be applied,...
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#4
Determine whether the given value is from a discrete or continuous data set When a limo is randomly selected, it is found to have enough room to seat 2 people. Choose the correct answer below O A. It is from a continuous data set because the number of possible values is infinite and not countable O B. tt is from a continuous data set because the number of possible values is infinite and countable ° C. It is from...
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