= g(b).Define h on h(x) = [a,c] by [f(x), a≤x≤b (g(x), b

Q: Let f(x) be a continuous function on (-00,0) and f"(x) = (-4x + 5)e4x. The function f(x) has an…

A:

Q: Suppose  f ( 200 , 300 ) = 1000and ∂ f ∂ x ( 200 , 300 ) = 12 and ∂ f ∂ y ( 200 , 300 ) = 10.…

A: Given, f(200,300)=1000 ∂f∂x(200,300)=12∂f∂y(200,300)=10

Q: Suppose f: (0, 1)→ (0, 1) is a surjective monotonic function. True or false: The function f is…

A: f: 0,1→0,1 is a surjective monotonic function.

Q: Show that if f(x) is continuous in(a, b),then there exists a point in(a, b) such that…

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Q: On what domain is the function f(x) = 3 + V5x – 20 continuous?

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Q: ( 2x -. Is g(x) continuous at 2?

A:

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: Define 1 if x 2 Determine the values of a and b such that f(x) is continuous for all x.

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Q: Justify that 12-21-3 if x + 3, f(x) = 4 I-3 if x = 3

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Q: Let f:[0,1]→R, be the function defined by, f(x)=|x-1/2|. Show that f is continuous and conclude that…

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Q: f(x) = x² - 2, x + 4, O true false x 3 is continuous everywhere.

A: f(x) = ( x2-2, x<=3            x+4, x>3

Q: If f is continuous, then b+c f(x)dx = ] -S Fx - c)dx f(x – a+c

A: Translation along the horizontal axis can be obtained using the transformation rule x→x-a on the…

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: Show that f is continuous on (∞ , -∞ )  .

A: we have to show that f(X) is continuous in (-∞,∞). f(x)=x2             if   x<1           x…

Q: Find numbers a and b, so that f is continuous at every point.  f(x)= 20 , x-1

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Q: Is the function f(x) = x + 1 from the set of integers to the set of integers onto?

A: For onto from set A to B, Every value of set B should exist atleast once in the function.

Q: If a function f(x) is not defined at x-a, then it is not continuous at an open interval (a, b) * O…

A: Given Statement is "False"

Q: Decide if f(x) is uniformly continuous on the interval. Explain

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Q: n a and b with f(c) = N. I thi

A: Mean value theorem: Rolles theorem If a real-valued function f is continuous on a proper  [a, b],…

Q: Consider the function f with domain (-2, : 3|22 – 1| if – 2 < x < 1 2x2 + 2x – 4 f(x) = 3 if x = 1…

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Q: Let esinx SoN f(t) dt and f is a continuous function, determine the value of f ()

A: If we have F(x)=∫0xf(t)dx then we have F'(x)=f(x). This is called the fundamental theorem of…

Q: show that f,given by f(x) x +0 )is continuous on R-{0}

A:

Q: If f is continuous on the interval [5, 12] and f(5) = 7 and f(12) = -2, then f must have at least…

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Q: Suppose that f(x) is a continuous function on the interval [0, 4] with f(0) = -10 and f(4) = 10.…

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Q: Suppose that a < b <c and f is continuous. Select all true statements. (a) f(x) dx = f(x) dx – f(x)…

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Q: Evaluate the function. f(x) = -52x + 3, for f(-1) f(-1) =

A: f(x)=-52x+3

Q: Find a and b so that f(x) is continuous if f (x) = Ⓒa = ²/1 b = 60 96 a = - ²/2 b = 29/4/20 -²/26 =…

A: