1. Which of the following statements is CORRECT? A. Continuous functions are not differentiable. B. Continuous functions do not have graphs. C. Continuous functions are differentiable D. Continuous functions have gaps on their graphs

Q: (9 pts.) Determine if the following function is continuous at x=-2. If not find the type of the…

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Q: Determine the discontinuities of the following functions and state why the function fails to be…

A: f(x)=x3+x2-17x+15x2+2x-15function is undefine when x2+2x-15 is become 0Let…

Q: Apply Rolle's theorem to the following functions on given interval

A: Consider the function fx=x2-2x-3x+2, -1,3 Here, the objective is to find c such that -1<c<3…

Q: On what intervals are the following functions continuous? ƒ(x) = x1/3

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Q: Suppose that f(x) is differentiable function such that f(1)=3 and f(1)=4. If g(x)= f(x) -, then what…

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Q: 2. ASSUME f(x) IS CONTINUOUS AND DIFFERENTIABLE ON AN OPEN INTERVAL AS GRAPHED. WHICH OF THESE…

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: Given the table of values for a continuous f(x) below, which of the following statements regarding…

A: Curve fitting and concavity

Q: For what value of a is the following function continuous at every x?

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Q: For what value of c is the function defined below continuous on (-∞, )? сх + 4, x 4. x > 4. f(x) = C…

A: f(x) = cx+4    ,  x<4cx2-4  ,  x≥4we have to check continuity on (-∞ , ∞)for a function to be…

Q: Suppose f(1) is continuous everywhere, and has the following values: 10 20 30 40 f(z) -4 9. 11 3. 7…

A: Given,  f(x) is continuos everywhere  f(x) has the following valuesx010203040f(x)-491137To…

Q: Is the following function continuous F(x)=x cot 5x

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Q: Let 1, if-3 <x s2 f(x) = %3D 4-x, if 2 < x<4 Without graphing, is f(x) continuous at x 2? Clearly…

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Q: On what intervals are the following functions continuous? k(x) = x-1/6

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Q: If a function is real and continuous in the region from a to b and f(a) and f(b) have opposite signs…

A: Given a real function with f(a) and f(b) having opposite sign.

Q: The lower limit in the lowest class interval should be equal to i. a. False O b. True

A: Frequency distribution table : A frequency distribution table is one approach to organize data to…

Q: Consider the function g :ℕ→ℝ  where  g(n) = 1 if n is odd and g(n) = 2 if n is even. Is g continuous…

A: Given function is g :ℕ→ℝ  where  g(n) = 1 if n is odd and g(n) = 2 if n is even.

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

A: Let f : X → Y be a continuous function. If X is disconnected then so is f(X).

Q: Suppose f : [a, b] → R is is continuous and such that fg = 0 for all continuous functions g : [a, b]…

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Q: State both the converse and the contrapositive of the assertion “Every differentiable function is…

A: We will make use of fundamental definition of these terms.

Q: For what value of k is the following a continuous function?

A: Function is continuous if   limx→2-f(x)=limx→2+f(x)=limx→2f(x)

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: Q3: determine whether following function are continuous ore not 4 X# 2 f(x): x-2 4 X = 2

A: To determine whether the below function is continuous or not. fx=x2−4x−2,       x≠24,…

Q: What values must a and b take for f to be continuous everywhere?

A: Given that the function fx=ax1+4x2 ,      x&lt;0b    ,                     x=0tan-1xx ,…

Q: 1. Write the conditions a function has to meet in order to be continuous at point a. a) b)

A: A function f(x) has to meet these conditions in order to be continuous at any point a

Q: B- If f(x) = is continuous at x = Find A? |Ax2 x2

A: The explanation of the answer as follows

Q: 5. Consider the function g(x)=1 a) For what values of x is g(x) continuous? b) For what values of x…

A: In the question we have to find where function is continuous and differentiable.

Q: Let f(x) = −2/x and g be the function defined b)Is f . g continuous at x = 3? If not, does…

A: limit of the composite function

Q: Let f(x) = { if x - 4 m= mx 6 - If f(x) is a function which is continuous everywhere, then we must…

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Q: On what intervals are the following functions continuous? g(x) = x3/4

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Q: Which of the following is a function that has a jump discontinuity at x = 2 and a removable…

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Q: Suppose that a state's income tax code states that the tax liability on x dollars of taxable income…

A: Given T(x)=0if x≤00.14if 0&lt;x&lt;10,0000.21x+cif 10,000≤x

Q: Suppose f(x) is continuous everywhere, and has the following values: 10 20 30 40 f(x) 4 10 8 5 5…

A: f(x) is continuous everywhere and has the following value: x 0 10 20 30 40 f(x) 4 10 8 5 5

Q: Answer the following True or False: If f(x) is defined and continuous on the open interval (a,b),…

A: The Extreme Value Theorem states that  If f(x) is defined and continuous on the closed interval [a,…

Q: For what values of a and b is -2, - b, -1 < x < 1 3, f(x) = ах continuous at every x?

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Q: For what value of the constant c is the function f(x) continuous at x = 1 Seter-2, | In (x) + 6, if…

A: We will use concept of left hand limit and right hand limit in this problem.

Q: On what intervals are the following functions continuous? a.ƒ(x) = x^(1/3) b. h(x) = x^(-2/3)

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Q: Which of the following functions are continuous? Why do you think they are continuous? hix fix

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Q: Decide if the following function is continuous using limits. x1. 2х g(x)= 3

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Q: Suppose f(x) is continuous everywhere, and has the following values: 10 20 30 40 f(x) 9. 13 2 3 What…

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Q: Find a value for the constant k, if possible, that kæ? if x 2 Is the function f(x) = 1 continuous…

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Q: 3. Which of the following functions is continuous?

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Q: Answer the following statements true or false. 8.1 The sum of continuous functions is continuous.…

A: Here we have to state whether the statement is true or false.

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

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Q: On which of the following intervals is f(x) А. (2, +) В.[1, 2] C. [2, +∞) D. (-30, +∞) continuous?

A: We will solve the problem

Q: Is the following variable discrete or continuous: The length of time of a phone call. Discrete…

A: 4. Continuous variable: When the variables take values on interval scale it is termed as continuous…

Q: Suppose f(x) is continuous everywhere, and has the following values: 10 20 30 40 f(x) - 2 7 10 - 4 7…

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

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Q: ⎪ ⎨ ⎪ ⎧x^2 − 1 , − 1 ≤ x < 0 2x , 0 < x < 1 1 , x = 1 −2x + 4 , 1 < x < 2 0 , 2 < x < 3 a) Is f…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.