Q3/ A) Decide if the following function is continuous using limits. 2х x<1, x=1, 3x+3 x>1.

Q: Suppose that lim (x,y)→(3,1) f(x,y) = 6. What can you say about the value of f (3,1)? What if f is…

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Q: х+ 2 if x 0

A: The given function is  f(x) = x+2ifx&lt;02x-2ifx≥0

Q: What three conditions must be met for a function ƒ to be continuous at the point (a, b)?

A: Continuity at points: The points of continuity are the points where a function exist and has some…

Q: When is a function continuous over a closed interval?

A: A function is continuous over a closed interval when it is defined at all points in the interval…

Q: The limit as x goes to zero of x-1 exists.   True or False?

A: We need to say whether the given statement, “The limit as x goes to zero of x-1 exists.” is true or…

Q: nuous

A: The function f is continuous at some point c of its domain if the limit of f(x), as x approaches c…

Q: Q4: Use the limit definition to compute the derivative, f(x), for 2.F(x) = Vx³ – x

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Q: What conditions must be satisfied by a function if it is to be continuous at an interior point of…

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Q: Describe a case where f(x) has a limit but is not continuous?

A: We know, if the left-hand limit is equal to the right-hand limit, then the limit of the function…

Q: 32? And are

A: {x2                               if x&lt;-2f(x)={x1/5                           if…

Q: Determine the whether the function is continuous at x=-2. Justify your answer 2x+7 if xS-2 using the…

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Q: Q4: Use the limit definition to compute the derivative, f(x), for 2 1.F(x) = xi

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Q: Is the function f(x) : 1 continuous or discontinuous on [2,+∞)? Vx - 2 Is the function f(x) : 1…

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

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Q: Express the limit as a definite integral on the given interval. n X;* -Дх, [1, 9] lim (x;*)² + 4 n-…

A: limn→∞∑i=1nxi*xi*2+4∆x,    1, 9 Here, fx=xx2+4, a, b=1, 9

Q: 57. Compute the derivative of f(x) = x3/2 using the limit definition. Hint: Show that f(x +h) – f(x)…

A: To show that the derivative of the given function by using limit definition is

Q: Evaluate the limitlimx→0+x sin(x) + x^2/ x^2

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Q: 7. If a continuous, differentiable function f has zeroes at x = -4, x = 1, and x = 2, what can you…

A: Mean value theorem relates average rate of change of a function over an interval to its…

Q: Use the definition of continuity and the properties of limits to show that the function is…

A: A function is continuous in an interval if is continuous on every point of the interval. Now, a…

Q: Find the left- and right-hand limits of the function fin Figure at x = 0, 2, 4. State whether f is…

A: Given-  To Find- The left- and right-hand limits of the function from the given Figure at x=0,x=2…

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: Determine whether the function is continuous at the given points. x+2 if x22 : 2,0 x if x<2 f(x) =…

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Q: Q4: Use the limit definition to compute the derivative, f(x), for 1.F(x) = x3 2.F(x) = = Vx3 - x

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Q: Is the function 1 >-{ f(x) = √x x3 x < 0 0 ≤ x ≤ 1 piecewise continuous or piecewise smooth on [-1,…

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Q: 28. Use the limit definition, lim 7 (x+h)- f(x) to determine the derivative of x-1. [Value of 4] h0

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Q: Give an example of a function that is continuous on (-∞,0) U (0,1] U [1,0). se limits and theory…

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Q: Use use the limit definition of the derivative to show that f(x) has the qiven denvative. f(x)= _2…

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Q: The function is continuous from the right at x = 2. Select one: True False f(x) = x+ 2 x². x < 2 x22

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Q: Sketch the graph of a continuous function on [0, 2] forwhich the Trapezoidal Rule with n = 2 is more…

A: The midpoint rule is a method of finding the area under a curve. We use the midpoint of each…

Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=…

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Q: Find the largest open interval using the tools of calculus where the function is changing as…

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Q: 2) If possible, give an example of where a function is continuous at a point but not differentiable…

A: Continuity of a function is the characteristic of a function by virtue of which, the graphical form…

Q: 7. Where is f(x.y)= continuous? Do not just write an answer, show your work or give any necessary…

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Q: Find the intervals on which the function is continuous. f (x) = { %3D 3, x = 2

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Q: find the value of c that make the function continuous

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Q: 2. Is the function f(x) =² continuous on the closed interval [-1, 1] ? Draw its graph illustrating…

A: Given problem:- Is the function ƒ(x) = 3/x continuous on the closed interval[−1, 1]? Draw its graph…

Q: Consider the following function and closed interval. f(x) = x3 - 4x2 – 16x + 5, [-4, 4] Is f…

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Q: 4) Use the Limit Definition of a derivative to find f '(3) if f(x): %3D 5-x

A: Given:- f(x) =2/(5-x)  To find:- Use limit Definition of a derivative to find f'(3)

Q: 1. Let f(x) = 2 %3D Use the limit definition of the derivative to compute f'(-1). X+3

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Q: Show that the function xsin f(x)%D 0, When x 0 is continuous but not differenti able at x = 0 When x…

A: Let f be a function defined in the neighbourhood of 'a'. Then the function f is said to be…

Q: Would it be possible for a function to be continuous on [0,2) but not on [0,2]?

A: Let us consider the function f(x) =(x+4)/(x-2) .

Q: Give a formula of a continuous function that is differentiable except at 0.

A: Consider the provided question, For a function to be continuous at a point x=a, we say that the same…

Q: Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0. 1]…

A: Given problem:- Use Intermediate Value Theorem to explain why the function has a zero in the given…

Q: 2) Use the definition of the derivative f(x+h)-f(x) lim hー→0 to find the derivative of f(x) =…

A: Our objective is to find the derivative using definition.

Q: Q4: Use the limit definition to compute the derivative, f'(x), for 2 1.F(x) = x3 2.F(x) = Vx³ – x

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Q: Find the limit for the following functions: x-sinx 1-lim, x-Vx² + 2x 2- lim,-o

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Q: Suppose fx) is continuous on the interval [0,10] and that f(x) = 0 only when x = 4. If f(5)< 0, what…

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Q: a function is continuous at x = c, then the limit exists as x approaches c. If the domain of a…

A: a. If a function is continuous at x = c, then the limit exists as x approaches c By the definition…

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.