Please explain the question clearly with all the options(a Let f = C(R) such that f is an infinitesimal of order 3 with respect to x-3, as x→ 3. It's true that

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

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Q: 02: Let f(x)= x' – 7x+ 2, 0sxs1. 1. Show that f(x) has exactly one real root in the indicated…

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Q: 2. Prove: Let ƒ : R → R be a continuous function satisfying f(x) = 0 for all rational numbers x.…

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Q: Show that the real-valued function f: R → R defined by f(x) = x° x E R. 3x2 + 3x + 1 increases for…

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Q: 3. Let f : R→R be a function defined by f(r) = 2x + 1. Is this function (only) injective, (only)…

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Q: 1. Describe all functions f such that f(r) ar² + bx +c and f(1) = 2 and f(-1) = 6.

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Q: 9) Use the Intermediate Value Theorem to prove that there is a number c, such that, Ac)=-1 for the…

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Q: ample 23: Show that the function f(x)=1-1-x is continuous on the interval [-1. 11.

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Q: Show that if f"(x) < 0 for x ∈ [a, b], then 1/2[f(a) + f(b)] < favg < f[(a+b)/2]

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Q: Select the following functions that are bijective. ƒ₂: R → R, ƒ₂(x) = 14 f₂: R → R, f₂(x) = x f₁: R…

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A: given function To find: continuity of the function at x=1

Q: uestion 6: Suppose f: N N has the rule f(n) = 3n²-1. Determine whether f is 1-1.

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Q: Provide an example of a function that is a bijection from (0, 2) to R. Prove that the function you…

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