If f and g are continuous and f(2) > g(z) for a

Q: f is continuous iff f-1(E) is closed

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Q: Iff and g are continuous on [a,b] and f(x) ≥ g(x) for all x € [a,b] th then A True B False [ f(x)dxz…

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Q: 1. Supposef is a continuous function on x 2 0,f'exists for x> 0, f(0) = 0 and f'is monotonically…

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Q: If f and g are continuous and Jf(x)dx = Jg(x)dx, then f(x) = g(x). Select one: True O False

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Q: 9. If y = f(x) is a continuous function at a point x = c in its domain, then (a) y = f(x) is a…

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Q: Show that if f: A-> B is continuous and A is compavt then f(A) is also compact

A: Let , f : A →B be continuous function. Here , A is compact set. We need to prove that , f(A) is also…

Q: If f(x) is continuous on the interval [a, b] and a <c < b, | f(x) dæ is equal to then

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Q: 10 If f is a continuous function and F'(x)=f(x) for all x € R, then x)dx=?

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Q: Suppose that ƒ is continuous in [0,1] and that f(x) E [0, 1] for all x. Show that f(x) = x for some…

A: Given that f:0,1→0,1 is continuous on 0,1. To show fx=x for some x∈0,1

Q: If f(x) is continuous everywhere, then If(x)| is continuous everywhere. TRUE O FALSE

A: If f(x) is continuous everywhere, then |f(x)| is continuous everywhere.True of false.

Q: =f and g are continuous on [a,b], then [*[f(x) + g(x)]dx = f(x) [ √° g(x) f(x)dx+ Sº g(x)dx (A) True…

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Q: If f(x) is continuous at x = c then f'(c) exists. True False

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Q: Find the value of m such that g(x) = {x+5 , if x ≤ m} and g(x) = {2x - 3 , if x > m} is continuous…

A: Function limit and continuity

Q: If f(x) is differentiable and strictly increasing on R, then f'(x) > 0 for all x.

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Q: 2. Show that if f : R → R is continuous on R and f(r) = 0 for all r E Q then f(r) = 0 for all x E R.

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Q: D. Prove that f(x) = |x - 6| is continuous at all points c in R.

A: Given function is fx=x−6. We have to prove that the function fx=x−6 is continuous at all point c in…

Q: If f: X →Y is continuous and E C Y is closed, then f-(E) must be: - Closed Open None of these

A: The given function: f:X→Y is continuous. That is, f(X)=Y is continuous. Then, E is the subset of Y…

Q: ) If f(x) = (0 <* < 1) (-1 < * < 0) expand f(x) in the form c,P(x).

A: According to our company policy i am supposed to answer ony one question at a time.  For the rest…

Q: a continuous function f such that f(4) = 4, f'(4) = 0, ƒ'"(x) 4 is:

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Q: If f(g(x)) is continuous at 0, then g(x) is continuous at 0  true or false

A: Given that If f(g(x)) is continuous at 0, then g(x) is continuous at 0

Q: [0, 4). 4. Prove that f(x) = x² is both uniformly continuous and continuous on

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Q: If a function f(x) is not defined at x-c, then it is not continuous at a close interval [a, c). * O…

A: We know that function is continuous at c if the 1) f(c) is defined 2)limit of f(x) exist, Here…

Q: Suppose f is a continuous function with x = a in its domain. Part 2 of the Fundamental Theorem of…

A: Note:- As per our guidelines, We’ll answer the first question since the exact one wasn’t specified.…

Q: Suppose f and g are two continuous functions on [a,b] and that f(a) g(b). Show that f(x) = g(x) for…

A: Suppose fand gare two continuous functions on [a, b] and f(a) &lt;g(a) but  f(b) &gt;g(b).  Show…

Q: Sßx² – 3 (Вх + 2 if (b) Suppose that f(x) if Find the value of ß so that f(x) is continuous…

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Q: If f:X - Y is a continuous function then f- (V) is open in X for every open set V in Y. True False

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Q: 2: If f(x) and g(x) are continuous on (a,b]and if f =[s . Prove that 3cela,b] such that f(c)=g(c).…

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Q: Suppose f and g are continuous functions on the interval [a, b], then SEAFX) – g(x)) dx = [." f(x)dx…

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Q: Suppose that f, g and g' are continuous on the interval I = {x : a <x < b}. Show that f f (x)dg(x)…

A: Given that the functions f,g and g' is a continuous function on the interval defined as  I=x:a≤x≤b…

Q: Iff is continuous on [a,b], then [xf(x) dx = x = xf²f(x) A True B) False f(x) dx

A: We will solve the problem

Q: (2х + 6, хS \x² + 3, x > Finition of continuity. f(x) =

A: Given,                  f(x) = 2x+6x≤0x2+3x&gt;0Now,                LHL = 6 And        RHL = 3Here,…

Q: 7. Suppose f is a continuous function on [a, b] and Sf(x)g(x) dx =0 for every continuous function g.…

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Q: If function f(x) and g(x) are continuous everywhere and f(1)=2, f(3)= -4, f(4)=8, g(0)=4, g(3)= -6,…

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Q: 4. Suppose that f is continuous on a closed interval [a, b] and differentiable on the open interval…

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Q: 4. If continuous function f:[0,1] U (2,3) → R is one-to-one, is f also continuous? 1

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Q: 1. Determine whether k(x) is continuous at a = 3, where x + 3, x 2.

A: Left-hand limit of f(x) at x=a is represented by limx→a- f(x) and it can also written as limh→0+…

Q: Find all values of a such that f is continuous on R: |x + 1 if x a

A: For a continuous function LHL ( left hand limt) should be equal to RHL (right hand limit)

Q: If n is a positive even integer and f(x) = Vx, then f is continuous everywhere. True False

A: Given that n is a positive integer and f(x)=(x)^1/n.

Q: If f is a continuous function on [a, b], and if f (a) = -2 and ƒ (b) = 2, then there exists a real…

A: Hi, you can find the answer in the handwritten form.  Given f(a)=-2  f(b)= 2

Q: If f(x) is differentiable at c, then there exists d > 0 such that f(x) is continuous in (c – 8, c+…

A: We have to define it is true or not

Q: True or false: Let f(x) be a continuous function. Suppose that f(x)dx converges for some real number…

A: We have used some properties of integration.

Q: 4. Let A := (0, 1] and let f : A → R be defined by f(x) = !. Prove that f is continuous on A.

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Q: If f(x) is a function such that the limit of f(x) as x approaches a does not exist, then f(x) is not…

A: Let's find.

Q: If ƒ(x) is continuous [-00,b]then on ſf(x)dx= lim [ ƒ (x)dx а. a a

A: Explanation of the solution is given below...

Q: If f is a continuous function on R with (1) > 0 and f(4) < 0, then there exists a number c between 1…

A: In this question, we need to check whether the given function is true or false.

Q: Suppose f(x) is a bounded real - valued function on [a.b) such that fela,b] . Does it follows that…

A: A function is bounded in [a,b] if it can't achieve value beyond a and b. i.e.maximum acheivable…

Q: If f is positive-valued continuous decreasing function and lim - S(x) = 0 then J F(x)dx diverges…

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Q: Let y'"+p(x)y'+q(x)y=g(x) (2)and y"+p(x)y'+q(x)y= 0(3) where p,q and g are continuous on R. Indicate…

A: Since here explanation is not required so I can write only true and false.

Q: If f:R → R is continuous at both 2 and 4, then f must be continuous at some c E (2,4). Select one:…

A: Consider the function f:R→R, that is continuous at both the points 2 and 4. Let there be a point c…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: