Questions from Calculus


Q: Use a graphing utility to evaluate / for several values

Use a graphing utility to evaluate for several values of n. What do you notice?

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Q: Use a graphing utility to evaluate / for several values

Use a graphing utility to evaluate for several values of n. What do you notice?

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Q: Prove that if the limit of f(x) as x

Prove that if the limit of f(x) as x approaches c exists, then the limit must be unique. [Hint: Let / f(x) = L1 and / f(x) = L2 and prove that L1 = L2.]

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Q: Consider the line f(x) = mx + b,

Consider the line f(x) = mx + b, where m ≠ 0. Use the ε-δ definition of limit to prove that / f(x) = mc + b.

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Q: Prove that / is equivalent to /

Prove that is equivalent to

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Q: Given that / prove that there exists an open interval

Given that prove that there exists an open interval (a, b) containing 0 such that (3x + 1)(3x − 1)x2 + 0.01 > 0 for all x ≠ 0 in (a, b). / exists an open interv...

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Q: Inscribe a rectangle of base b and height h in a circle

Inscribe a rectangle of base b and height h in a circle of radius one, and inscribe an isosceles triangle in a region of the circle cut off by one base of the rectangle (with that side as the base of...

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Q: A right circular cone has base of radius 1 and height 3

A right circular cone has base of radius 1 and height 3. A cube is inscribed in the cone so that one face of the cube is contained in the base of the cone. What is the side-length of the cube?

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Q: Describe how to find the limit of a polynomial function p(

Describe how to find the limit of a polynomial function p(x) as x approaches c.

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Q: What is meant by an indeterminate form?

What is meant by an indeterminate form?

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