Let f(x) be a function and be R. f is continuous at r = b if and only if : 4.1 ......... 4.2 4.3

Q: at

A: We have to choose the correct option from the given options according to the given information

Q: Let f : R² → R defined by f((x1, x2)) = x1 - x2. Then determine if is Lipschitz continuous(if it is,…

A:

Q: Q2. Let f:R- R be a function such that f(x) = x sin| f is defined at x, , where the value of d…

A: Topic- Limits

Q: f(x) = V3x–1 c = 1

A: As we know that; If the function fx is continuous at x=c then, limx→c-fx=limx→c+fx=finite…

Q: Let f be defined as follows: Sx+5 for x> 5, f(x) = Зах for x <5 } For what value of a is the…

A: A function f is continuous at a if limx→af(x)=f(a).

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

A:

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

A:

Q: If f(1) = 2, f(4) = 7, f'(1) = 5, f'(4) 3, and f"(x) is continuous, what is x f"(x) dx? %3D

A: Given: f(1)=2f(4)=7f'(1)=5f'(4)=3I=∫14xf''(x)dx=?

Q: ALL of the following are properties of continuous functions except a. h/b is continuous at x = a…

A: given

Q: Determine the interval(s) where f(x) = is continuous. 1- In(1/r)

A: It is given that, f(x)=11-ln1/x   A function is said to continuous in an interval in which it is…

Q: Is the following statement correct? If the function is continuous on R then the constants a and b…

A: It is not necessarily correct that every continuous function on R take the value 2&amp; -2…

Q: Determine whether the statement is true or false. f(t) : e-t- et 2 is continuous everywhere. O True…

A: Given that f(t)=2e-t-et Now, e-t-et =0 gives1et=etor, 1=e2tor, et=1or, t=0

Q: c =

A:

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

A:

Q: For what values of b is - b b + 1' g(x) x? + b, x > 0 continuous at every x?

A:

Q: Find a value of x, if any, at which f(x) = x + 2 - is not continuous. x2 + 4 If f(x) is continuous…

A:

Q: Find a value of x, if any, at which f (x) = Vx – 125 is not continuous. If f(x) is continuous for…

A:

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

A:

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 if x V2. Prove or disprove that f is continuous.

A:

Q: If f is continuous on [a, b], then the horizontal line y = k for every k between f (a) and f (b)…

A: If function 'f'  is continuous on closed interval [a, b], and if f(a)≠ f(b), then for any number k…

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 X is continuous with f(x) = x/2 from 0 to 2. What are the values of f(1) and P(X=1)? 1/2 and…

A: Given,f(x)=x2 ; 0&lt;x&lt;2

Q: Let f : X 'n Y be a continuous function. If X is disconnected then so is f(X). True False

A: As image of a connected set is connected in of every continuous function.

Q: All the following functions have continuous extension at x = 0 EXCEPT. Select one: a. None of them…

A:

Q: Let f : R → R, and let x E R. Prove that f is continuous at x i and only if for every e > 0 there…

A: We have to provex that  epsilon delta definition of continuity:

Q: Let f(x) = CX– 2, x > I lx+ 8, x < 1 For what value of c is f(x) continuous on (-00, 0)

A:

Q: If a function f is not defined at x = a then it is not continuous at x = a. Select one: O True O…

A: As we know that a function f(x) is said to be continuous at x=a when the right-hand limit and…

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).…

A:

Q: If a function f is not differentiable at x = a E R, then f is not a differentiable function. True O…

A: The given statement is if a function f is not differentiable at x=a∈ℝ, then f is not a…

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

A:

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: (a) Prove that if m ₹ N, then the function f(x) = xm is continuous on R.

A: We have to prove that, the function f(x) = xm,   m∈ℕ  is continuous on ℝ.

Q: 1 - is continuous at a. f If f(x) 0 for all x in the interval I, and f is continuous at a in I then…

A: 1/f is rational function this is discontinous where either f is discontinous or f is zero  But f is…

Q: Which of the following functions is continuous on the interval (-0, +)? …* f(x) = Vx² – 1 (A f(x) =…

A:

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

A:

Q: Find the value/s of a such that the function f is continuous everywhere.

A:

Q: Let f be a function that is continuous on the closed interval [1, 5] with f ( 1) = 10 and f (5) =…

A:

Q: On which of the following interval is f(x) S O (0, +∞0) ○ (2, +∞) O [2, +∞0) 0 (-∞, +∞0) 1 x-2…

A: We will the fact that root value should be positive.

Q: 3. For what value of b, f(x) is continuous at every x? f(x) = {, x -2

A: Given that, fx=x         x&lt;-2bx2      x≥-2

Q: 86. If f is continuous and f (x) dx = 4, finc

A: Given that: ∫09f(x)dx=4

Q: 4) Is the following functions continuous? for x < 1, d(x)= x- 2 for 1 < x.

A:

Q: For every continuous function f(x) defined on symmetric interval [a,b]. If f(x) is an even function…

A: Here, the given function f(x) is even. So, f(-x)=f(x)

Q: 4. Use the limit definition of the derivative to test whether the following function f(x), given by…

A:

Q: Suppose the function ƒ has the property that IS(x) – S()| < |x -|| for each pair of points x, t in…

A:

Q: Is the following statement correct? If the function f is continuous at x=1, then the constant a…

A:

Q: (e) If f(x) is continuous at x = 0, then what is the value of n: if 20 if x=0 f(x)=\ 38

A:

Q: The function f(x) is continuous everywhere. FALSE O TRUE 3.

A:

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: 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: