If definition 1 is for big O notation, (Definition 1. Let g be a non-negative function near x0, which can be a finite number or ±∞. We say that f=O(g)near x0 if |f(x)|≤Cg(x) near x0, where C is a constant) and Definition 2 is for little o notation, ( We say that f=o(g) near x0 if limx→x0 f(x)/g(x) =0, Which of the following is correct? sinx=O(|x|) near x=0 provided choices  do not fit sinx=o(x2) near x=0 sinx=O(x2) near x=0 sinx=o(x)near x=0

Q: consist of only one graph): (a) f(-2) = 2 (b) lim f(r) = 0 %3D (c) lim f(r) = 1 I-3- (d) lim f(r) =…

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Q: q). State the equations of the horizontal asymptotes. r). State the equations of the vertical…

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Q: 2. Find all values k that make this function continuous at x = 3. Зх — 9 - if x > 3 f(x) = x² – 3x…

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Q: f(x): = ax² + x - b, ax + b, 2ax - 7, (a) Find the values of a and b such that f is continuous on…

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Q: In (x+1) lim log, x f)

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Q: 8. The function g(x) is written as: 5x + 3 if x 1 Find lim g(1+x²) x-0 g(x)= =

A: To find the limit of g(1+x^2) as x approaches to 0.

Q: Consider the following function: - 4 if x 3 Find the values of a and b that make f continuous…

A: The function is continuous every where, if it is continuous at each point in the domain. The…

Q: 7. Assume that f(x) is the original function. Describe how each of the following tran- forms f(x).…

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Q: 1. Determine and completely simplify f(x + h) – f(x) for f(x) = -7 Зх + 1

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Q: 4. Graph the piecewise function 3 if -1 2

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Q: 6. Graph the piecewise defined function. 1x+4] if x2

A: We will make a table for each piece of the function y=|x+4| , x < -3 x -3 -4 -5 -6 y 1 0 1 2…

Q: 20. List all of the transformations that are needed to graph the given function using f(x) = x² f(x)…

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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.