For a continuous function f(x) on the set 2 [- 5,2], the net area Tx)dx must be -5 always positive Select one: True OFalse

Q: What is the difference between discrete and continuous variables?

A: Discrete variables takes countable, finite or exact values in a given interval where as continuous…

Q: Give examples of functions that do not have any fixed points, but do have these char- acteristics:…

A: We know that a function f:A→A is said to have a fixed point if there exists x∈A such that fx=x. In…

Q: 2x - 3x + 13x+a if x#2 f(x) = . X-2 b if x = 2

A: Solution:- It is give that f(x) is continuous at x=2  and the given function is  f(x)=…

Q: ax +b, if15メ<2 Find the values of a and b so that the following function is continuous evergwhere- x…

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Q: Provide an example of a function which is continuous on all of R and differentiable on all of R…

A: The function is y=x+4 (shown in the figure above)

Q: When is a function continuous over a closed interval?

A: A function is continuous over a closed interval when it is defined at all points in the interval…

Q: Let f(x) = { *, if x= 2 ; for the eax if x + 2 function to be continuous at x = 2 the value of a is

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Q: Show that f1x2 Vin x is right-continuous at x = 1.

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Q: For what values of a and b is the function f continuous on (- 00,00)? (Write only the values of a…

A: For what values of a and b the function f continuous on -∞,∞            a-3x     if x&lt;-1f(x)= 4a…

Q: If f(z) <0 for all real numbers z then f is decreasing on (-o, 00) Select one: O a. False O b. True

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Q: 5. (a) Let f: S T be a function, and A CT and BCT be subsets. Show that (A-B) = f-1(A) - f-(B). ww

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Q: find lim ( Sx²+ax-Jxb% 2. Xつや

A: Solution  limx→∞Axn=0 , where A is constant and n&gt;0

Q: Find x-intercepts of the function: x2 – 9 f (x) = Зх + 1 Select one: O a.x = 3 O b.x= -3, x= 3 C. X=…

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Q: A function fis defined by Sx. x<-2 g(x) = bx, x z -2 bx².

A: It is evident that we need to find the value of b if g(x) is continuous. Now,…

Q: Are these functions injective or surjective?  f : R → R; f(x) = x^2,  f : R → Z; f(x) = bxc,  f :…

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Q: Find the value(s) of a and b for which f is continuous at -2: 3x³ - 7x² + 7 if x -2 f(x)

A: To find the values of a and b for which f is continuous at -2.fx=3x3-7x2+7 if x&lt;-2a+b if…

Q: Consider f = {(x, y) : x ∈ N and x + y = 5}. Write out some elements of f. What are the domain and…

A: Given: f={(x,y): x∈N and x+y=5} The domain of a function f(x) is the set of all values for which the…

Q: Construct a table of values to investigate If r so x? - 2 if x > -1 Jim f(x)tf f(x) = *--1

A: limx→-1 fx if fx=1xif x≤0x2-2if x&gt;-1  x -1.004 -1.002 -1 -0.998 -0.996 f(x) -0.9960 -0.9980…

Q: Suppose f is a continuous function on [a,b] and suppose that f(a) 0 What can you say about the…

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Q: Construct a continuous function that shows that the intervals [0,1] and [2,6] are homeomorphic.…

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Q: Construct a continuous function that shows that the intervals [0,1] and [2,6] are homeomorphic

A: In the given question we have to find a continuous function from the interval [0,1] to the interval…

Q: Evaluate 4. sec "xcosec"xdx

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Q: Please show all work:  Is f(x)= x2+3 continuous at x=1? Why or why not? (A rigorous mathematical…

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Q: y=(x) -6 Let f be the continuous function defined on [-6, 6] whose graph consists of a quarter…

A: Given: g be the function given by, g(x) = ∫-1x f(t) dt  To determine: (D) The absolute maximum value…

Q: how is it continuous?

A: The given two variable function is fx, y=x2+y2x2+y2&lt;11x2+y2≥1

Q: What is the sign-preserving property of continuous functions?

A: What is the sign-preserving property of continuous functions?

Q: For what value of the Constant c is the function F defined below continuous on (-00,00)? Fly= { Y²-C…

A: A function,

Q: f(x,y)= sin(x² + y²) + √√√9 - x² - y²

A: Note : The composition function " g∘f " of f and g  is continuous at a point "c" if f is continuous…