Draw a graph clearly showing the following:  no derivative but continuous (do this in two different ways) not continuous but the limit exists no limit but still in the domain

Q: Explain the differences between continuity and uniform continuity with the help of examples shown on…

A: See, continuity is defined at a point p, whereas uniform continuity is defined on a set A. That…

Q: The goal of this problem is to compute the value of the derivative at a point for several different…

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Q: \(d\) is a metric on \(X\). Show that \(\rho : X^2 \to [0,\infty)\) defined by \[ \rho(x,y) =…

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Q: Sketch the graph of a function f  that is continuouson [1, 5] and has the given properties.…

A: Sketch the graph of a function that is continuous defined on the interval [1,5] having the following…

Q: State the function and the number: f(x) = a =

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Q: Calculate the first first derivative justifies whether this is differentiable or not. Calculate the…

A: ∴ f(x) = 2x2ex is differentiable

Q: Use the limit definition of the derivative (or simple common sense using geometry) to find the slope…

A: We have to find the slope at the point x=-6 of the function f(x) using limit definition of the…

Q: lim t→1 t4 + 1-2 t t-1

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Q: 1). Does the left-side limit of the difference quotient of the function g(w)=|w| exist at w=0? If it…

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Q: 3. g(x) x² +5

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Q: write me an equation for a graph that is defined at x=-2 has a limit at x=-2 but is not continuous…

A: The objective of the question is to find an equation of a function that is defined at x=-2, has a…

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.