Based on your work in part a, on what interval(s) is f(x) continuous?

Q: Find the x -values (if any) at which f(x) is not continuous, where (x-5

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Q: Describe the interval(s) on which the function f(x) = is continuous.

A: The given function fx=xx2+x+2 is in gxhxform. The numerator gx=x is continuous for all x∈-∞,∞ in its…

Q: (c) Suppose that ƒ hits every value between y = 0 and y = 1 on the interval [0, 1]. Must ƒ be…

A: A function is continuous when its graph is a single unbroken curve , that you could draw without…

Q: Is the function f(x) = > ` continuous at x = 0? Explain your answer. n=0

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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: Describe the interval(s) on which the function is continuous. f(x) = 3 − √x

A: Given function is

Q: Describe the interval(s) on which the function is continuous. f(x) = (x + 1)/√x

A: We can not have negative number inside the square root.  So, x≥0   And we can not have 0 in the…

Q: Describe the interval(s) on which the function is continuous. f(x) = sec x/4

A: The denominator can not be 0.

Q: Describe the interval(s) on which the function is continuous.

A: Given: fx=xx+3

Q: compute f ' (a) using the limit definition and find an equation of the tangent line to the graph of…

A: Given f(x)=x2-x The limit definition for derivative of a function is given as: Using the above…

Q: a) At how many points is f(z) discontinuous? b) At how many pints is f(z) not differentiable?

A: This is a calculus problem and I solved it in the next step.

Q: If f(x) is continuous in the interval [-2, 1], ƒ(−2) = −4, and f(1) = -1, can we use the…

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Q: Describe the interval(s) on which the function is continuous.

A: Given: Describe the interval(s) on which the function is continuous. f(x)=sec πx4Clearly from the…

Q: For what value of the constant c is the function f continuous on (-0, 00)? C =

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Q: Find the equation of the tangent line of f(x) = sqrt(x+1) at x = 0 using the definition of limits.

A: To find: The equation of tangent of line. Given: The function is f(x)=x+1. Concept used: Slope…

Q: use the limit definition to compute f'(a) and find an equation of the tangent line. f (x) = x3 + x,…

A: For a function f(x) the limit definition for derivative at x=a is f'(a)=limh→0f(a+h)-f(a)h. The…

Q: For which values of x is the function below NOT continuous?

A: To find out the values of x at which the function is discontinuous.

Q: What is the definition of f(x) is continuous at x = a? ||

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Q: If ƒ is differentiable at a, must ƒ be continuous at a?

A: we know that for a given function if it is differentiable at given point then it must be continuous…

Q: At what points are the functions continuous? x + 3 f(x) 2 - et

A: The given function is fx=x+32-ex

Q: , Use the limit definition of the derivative to prove the following special case of the Quotient…

A: Let f be a differentiable function. then its derivative is given by f'x=limh→0fx+h-fxh.

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line. f (x) = x3 + x,…

A: Anwer: f'(0)=1

Q: define the function at 5 so that it becomes continuous at 5.

A: First, we rationalize the function, so that it becomes continuous at 5 which is shown on the board

Q: Come up with an example of a continuous on [0, 2] function for which the trapezoidal rule is more…

A: Let us consider a continuous function fx=cosx for x∈0,2. fx is continuous on 0,2 Now, exact value of…

Q: show that the intermediate calue theorem applies on the indicated interval and find the value of c…

A: f(x)=x4-x2+3x+1 we know that f(x) is continuous on the given interval [0,1] lets find out f(0) when…

Q: f(a) = ca + 4 if a E (-∞, 2] I ca -4 if a e (2, 00) if a E (2, ∞)

A:

Q: Use the limit definition to compute f 1 (a) and find an equation of the tangent line. f (x) = x +…

A: For a function f(x) the limit definition for derivative at x=a is f'(a)=limh→0f(a+h)-f(a)h. For a…

Q: If f:R to {0,1} and I is an interval on which f has both values , the f has a discontinuity in I.…

A: Given that f has both 0 and 1 in its range.  This means there will be some x and y values for which…

Q: If f(3) = 15, f' is continuous, and I f'(t) dt = 24, what is the value of f(4)? %3D

A: In this question, f is a primitive function and we have to find f(4). So I am providing the…

Q: At which interval of x is the function of P(x)=(sqrt(1-x^2)) discontinous?

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Q: x = 0 f(x) sin z x +0 а) х — 0. ? b) х — 4т. ?

A:

Q: Where is f(a) not continuous?

A: Given:

Q: Since the simplified numerator, >0 for all X, we have "(x) > 0 x²-1>0 e ]x > and f"(x) < 0 X| < Thus…

A:

Q: What is the largest interval containing zero on which f (x) = sin x is one-to-one?

A: A function f: X -&gt; Y is said to be one-to-one, if the images of distinct elements of X under f…

Q: Suppose f(r) = (In z)e. What is f'(x)?

A: d/dx (f(x)g(x))= f(x)g'(x)+g(x)f'(x)

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A: given that  f(x)=tanx2

Q: Is f(x) = x |x| differentiable at x = 0? Provide a brief justification of your answer.

A: First it needs to be proved that fx=xx is continuous at x=0 limx→0-fx=limx→0xx=limx→0-x2=0…

Q: Determine if f is continuous at the indicated values. x = 0 f(x) = 1 sin x x + 0 a) x = 0. ? b) x =…

A: Given

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line.

A:

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

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Q: Use the limit definition to compute f '(a) and find an equation of the tangent line.

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Q: 3. What value of k would make f (x) continuous at x = 3 ? 3.

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Q: Find the value of a which makes the function below continuous on (-∞, ∞). f(t) = [a(x²/2) x < 1…

A: We will use the definition of continuity to solve this question.

Q: Is the signum function, f(x) = sgn x, continuous at x = 0?

A:

Q: Come up with an example of a continuous on [0, 2] function for which the trapezoidal rule is more…

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Q: If f(x) is continuous at x = c, then so is If (x)|.

A: To determine: The given statement is true or false. Given statement: If f(x) is continuous at x=c,…

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

A:

Q: Is the following functions continuous or not at z = 0?

A: To check whether the following function is continuous at z=0fz=Rez1+z

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.