Let f(x) 2x2+3 •given ɛ > 0,find M x2 such that if x > M we have |f (x) – 2| < ɛ. Conclude that f(x)has a limit of 2 as x → 00.

Q: 2. Sketch a graph of a quartic polynomial function y = fx) such that: € fu) > 0 when - 2 1

A: In the given question we have to draw the graph of a quadretic polynomial s.t f(x)&gt;0 when…

Q: For the function Sx² - x x² – if x 1 ’ evaluate the left and right limits as x → 1.

A: We can make it easier for you.

Q: 3. Let f(x) = x - r - 3x. Determine the interval(s) on which f(x) is increasing and the interval(s)…

A: To find the points of minima and maxima first we need to find the critical points of function by…

Q: Suppose a smooth function f(x) satisfies f(0) = 0, f(1) = 2, and that f[x0,x1,x2] = 1  for any three…

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Q: Q: Let f: R→R be given by f(x)= x +3 Find (a){x: f(x)= 28} (b) The pre-image of 39 and 2 under f.

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Q: 9) For each of the following functions, f(x), find all x-values on (-o, 0) at which f is not differ-…

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Q: If the given three vectors are coplanar, then find the value of x. A = i-2j + 3k, B = xj + 3k, C =…

A: A, B, C are coplanar.So

Q: B. Test whether the given function is continuous or not, and classify the discontinuity whether…

A: Given problem:-

Q: . Let f RR be defined by setting f(x) = x if x is rational and f(x) = 0 if x is irrational. Use the…

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Q: 6et-8) _6 if 0 8

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Q: If f(x) = x* + 7x² – 144, use Rolle's Theorem to find all the values of c in the interval [-3, 3]…

A: Given: f(x) = x4+7x2-144, interval [-3, 3]

Q: Let f(x) is defined as (kx² – 1, S (x) = x-1 Determine k so that the fur

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Q: The limit of f(x) = |1-x|/x-1, as x approaches 1 does not exist because: a. f(1) does not exist…

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Q: If g(x)=x and f(x) = e2x, what is the limit of the division of g(x) by f(x) as x 0o.

A: Given that:gx=x and fx=e2xTo find limit

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.