Let f(x)=x'e* the value of lim [f (x) is: 4 x 1 a) 1 b) | e

Q: Let ce (a, b). If ƒ (x) is a function that is continuous at c, then lim,e- [f (x)] = lim,»c+ [f…

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Q: Given that f(x) = 2x² +1, find:“ f(x+h)- f(x) f(x+h)– f(x). lim h→0 h h

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Q: 3. Use the Squeeze theorem to prove that lim x- sin () = 0. Explain thoroughly. x0 (Hint: Use f(x) =…

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Q: Sx² 15 a. Find lim f(x). if x + 2 2. Let f(x) = } if x = 2 X→2 b. Find f(2). Is f(x) continuous at x…

A: Proceed as shown below...

Q: If lim f(x) = L, then f(a) = L. A) True B) False

A: We can find the value as below

Q: Evaluate the limit lim f(t) where ƒ(t) = = lim f(t) = i 00-11 00-11 (9+17) 2 for t = 0.

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Q: If 3x − 1 ≤ f(x) ≤ x2 − 3x + 8 for x ≥ 0, find lim x→3 f(x).

A: Here we use sandwich theorem Also known as squeeze theoremThis theorem states that , if gx≤fx≤hx in…

Q: If lim f( x ) + f(a) ,then f(x) is at continuous , y = f(a) not continuous ,x = a continuous, x = a…

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Q: Assume that rs f(x) < 3r. Compute lim f (x)

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Q: 1. v₁ = (4, −2, 6, −4), V₂ = (6, −3, 9, −6)

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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.