Give an example of a function that is integrable on the interval [-1,1], but not continuous on [-1,1].  Explain.

Q: 2 2 x >1 4 2x> 2 4 x+ 2 b) f(x) = . 16 52x>4 x² + b 6 2 x > 5 1)is the above function continues at…

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Q: The summation of a constant is equal to the product of the cardinal of the index set and the…

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Q: ive 5 Real Life Application of Extreme Value Theorem (This is all about Calculus: Extreme Value…

A: claim- give 5 real life application of extreme value theorem 1) we can use Extreme value theorem in…

Q: Explain how you might differentiate a piecewise function like |x| When it's differentiable, for…

A: We can use the concept of calculus and function in order to solve the given question.

Q: Determine the interrals on which fIS increasing decreasing and constant. also state the domain and…

A: To find:- Need to find out intervals where function increasing, decreasing and constant Method:-…

Q: 3. There are two conditions that must be met in order for a function to be continuous, explain those…

A: See a function is continuous at a point a when these two conditions are satisfied,i) ii) Note that…

Q: a+11 if a 10

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Q: As the number of hours since you ate protein increases from 2 to 2.75 hours what is the average rate…

A: Given: At 2 hours B1=1100 mg/L At 2.75 hours B2=1025 mg/L

Q: (a) How many pairs (f, g) E F x F are there so that go f(1) = 1? Explain.

A: The main objective is to give explanation for part (a) why possible g  functions are 4^3.

Q: Determine whether the function is not differentiable using differentiability and continuity, and…

A: We have to find if the function is differentiable or not. First we will check the continuity by…

Q: "If a function is continuous at some point then it must be differentiable at that point". Do you…

A: To show whether the given statement is true or false .

Q: What is the zeros of this function?

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Q: Construct a continuous function that shows that the intervals [0,1] and [2,6] are homeomorphic.…

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Q: 0,x1 x+2,x<-1 f (x)= %3D 2,x2-1

A: Interval notation is a way to describe continuous sets of real numbers by the numbers that bound…

Q: f(x) = 523 -5x + b if r ≤ 9 if x > 9

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Q: Let f(x) = 6x¹ + 2x³. Select all intervals where f(x) is INCREASING, 0 (-∞, ¹²¹) ☐ (0, ∞0) 0(¹,0)…

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Q: Write the Intermediate Value Theorem for Continuous function?

A: Intermediate value theorem: Statement: The intermediate value theorem states that, If f is a…

Q: Use the definition to show that the function f(x) = → is continuous on the interval [c, o), %3D…

A: The given function is f(x)=1x2 .we have to show that f(x) is continuous on the intervel [c,∞)…

Q: All polynomial functions are continuous. * TRUE FALSE

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Q: == ² x + 17, √8x + 13, ①8 x> 8

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Q: Describe the increasing, decreasing, and constant behavior of the function. (Enter your answers…

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Q: There are 3 conditions that make a function continuous at a point.  Name the three conditions Give…

A: Definition: A function is said to be continuous at x = a provided all three of the following are…

Q: Create a piece-wise function that is NOT continuous and has domain (−∞, ∞)

A: Let f(x) be a piece wise function, that is not continuous and extends throughout the domain of real…

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.