Consider the continuous function h with h'(x). In(x) +6 3 3.1 Find and represent the domain of the function, using set notation.

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

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Q: Find c such that the function x2 – 9 x с is continuous everywhere. - С —

A: f(x) will be continuous at x=c. when value of the function at c , left hand limit of f(x) at c  and…

Q: Determine the domain of the function and prove that it is continuous on its domain using Theorems…

A: Given: f(x) = ln (9 - x 2) To determine: The domain of the function and prove that it is continuous…

Q: For the continuous function f(x), if f’(-4) does not exist, then x=-4 is a critical point.

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Q: 2. Let f (x) = x² + 3x – 5. а. Use the formal limit definition of the derivative to compute f'(x).

A: Given,          fx=x2+3x-5

Q: Determine the value of x of the continuous function: * (x – 1 x 3 f(x) = {3x – 3 Зх — (-4x + 3

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Q: is continuous or discontinuous at x = -4 using the three step continuit x + 6 x -4

A: We have to check continuity  of function

Q: Let f (x) = x² – 4. a. Find f'(x) using the formal limit definition of derivative. -

A: The formula of formal limit definition of derivative is  : lim h →0  [{f(x+h) - f(x)} / h ]

Q: 3x+8x74 F(x)=(7x-K x<4 X=4 11

A: Given f is continuous at x=4

Q: 9-x - S(x)= Vx- 6

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Q: Suppose that a continuous function g satisfies: g(x)dx = 42 and g(2x)dx = 3. %3D 2 Find æg(3x²)dx.

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Q: Using the (e- 6) definition, show that f(x) = 3x – 1 is continuous at point x = 1.

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Q: Consider the piecewise function: |x- 1| x² – 1' x <1 f(x) = (Ax² + 6, x 2 1 For what real number A…

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Q: Let f be a continuous function with f'(x) = 3x² Of has no relative maxima. 0x=0 0x=2 0x=1 - 6x. At…

A: f be a continuous function with f'x=3x2-6x

Q: Suppose that f(1) = 1, f(4) = 6, f (1) = 7, f '(4) = 5, and f " is continuous. Find the value of xf…

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Q: The function f(x)=(2-x)/(3) is continuous at

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Q: h(x) = { 3-2 -2 if x≤-1 Cx² + 4x if x>-1

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Q: Suppose that a continuous function g satisfies: g(x)dr = 30 and g(2x)dx = 3. 0. 2 Find r9(3x²)dx.

A: Suppose that a continuous function g satisfies: ∫03gxdx=30 and ∫06g2xdx=3. The, we have to find the…

Q: Find the values of k that make the function continuous. Jk² + 18x, x > -3 f (x) = kx, x < -3

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Q: 2) Consider the piecewise function: |x – 1| x² – 1' x 1 For what real number A is the function…

A: A function f(x) is continuous at x=a if the left-hand limit and the right-hand limit of the function…

Q: Suppose that a continuous function g satisfies: | g(x)dr = 24 and 9(2x)da = 21. 0. .2 Find

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Q: Show that f(x) = 2a + 3b is continuous, where a and b are constants

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Q: Consider the function f(x) = In(x) – arctan(2.x). 2 a. Determine all critical points in the domain…

A: We know that the critical points of a function are those points at which the first derivative is…

Q: Find the absolute minimum and absolute maximum values of f on the given interval. fx) =Dx -In(7x),…

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Q: For what value of a is x² -1, x< 3 f(x) 2ax, x2 3 continuous at every x?

A: Given function is Since, f(x) is continuous at every x, so f(x) is continuous at x=3.

Q: f(x) = Vx-3

A: Given function is fx=x-3.

Q: Sketch the graph of a continuous function y = f(x) such that : a. g(2) = 2,0 2, and g'(x) →-1* as…

A: (a)  Find the behavior for g (x).

Q: 6. Use the definition, determine whether the function g(x) = x = 2. Justify the conclusion. x² -…

A: The solution is given in the next step.

Q: Find the constant c that makes g continuous on (-0;0) x-2x-8 g(x) = a+1 if x+2 if X=-2

A: Continuity of a function at a point x=c : If function is defined at x=c and limx→c fx=fc then we can…

Q: Sketch the graph of a continuous function y =f(x) that satisfies the following conditions: 1. f'(x)…

A: This question is about graphing a function

Q: Consider the function (x)=x²+2x . Using the limit definition of the derivative, show that for any…

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Q: The function f(x)=/25-x' is contionous on

A: It is continuous function.

Q: Use the intermediate value theorem to show that f(x) = e-x2− x has at least one root in the interval…

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Q: Determine the value of x of the continuous function: * х — 1 f(x) = {3x – 3 (-4x + 3 x 3

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Q: Find c such that the function x ≤ c { is continuous everywhere. f(x) = x² - 3 X 6x 12 x > c -

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Q: Showthat fo= x| is Continuous evalyuhore- 1x1+1

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Q: Suppose that a continuous function g satisfies: | g(x)dx = 12 and g(2x)dx = 27. Find æg(3x²)dx.

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Q: 1. If f:(0, 3) → R is continuous, must its range be an open (possibly infinite) interval?

A: Given statement is : If f:(0, 3) → R is continuous, must its range be an open (possibly infinite)…

Q: Determine if g (x) = is continuous at x = 0

A: A function f(x) is continuous at x=a if, limx→af(x)=f(a). We try to evaluate limx→04-xx and f(0) and…

Q: A continuous real-valued function f (x) with f (a) ƒ (b) < 0 , has at least one root in [a, b]

A: This question is related to Real Analysis.

Q: Find m so that f(x) is continuous at x = 2. x +4 if x 2 -

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Q: If a function f is continuous at 0, show that g(x) = xf(x) is differentiable at 0 and find the value…

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Q: Suppose that a continuous function g satisfies: g(x)dx = 42 and | g(2x)dx = 12. 2 | #g(3x²)dx. Find

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Q: Draw the graph of a continuous function f(x) where f(-2) = 0, f(2) = 0, but there is no value c€…

A: Given: f(-2)=0 ;     f(2)=0but there exists at least one c∈-2, 2…

Q: øz (@) is a continuous function of o in the range -o < @< ∞.

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Q: Find the values of m and n that make f(x) continuous over (-∞, ∞): f(x) = m= n= 4 x-2 mx² - nx 2x -…

A: Topic- Limits and continuity

Q: Find c such that the function x c is continuous everywhere. x² – 8 f(x) = {

A: ANSWER : c = 5