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Practice Quiz 1b - (a What value of A if any makes this...

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Practice Quiz IB for Calculus I, MATH 1501 (I) Let f ( x ) be given by f ( x ) = x 1 + x 2 . (a) Find all x such that | f ( x ) - f (1) | < 1. (b) Find a δ ( ) > 0 such that | x - 1 | < δ ( ) ⇒ | f ( x ) - f (1) | < . and justify your answer. (II) Which of the following limits exist? If they don’t exist, explain why not. If they do, compute the value of the limit. (Note: In part (b), a is a parameter, and your answer will depend on a ). (a) lim x 0 1 x 1 1 + x 2 - 1 (b) lim x 0 cos( ax ) - sec( ax ) x 2 (c) lim x 1 sin x 2 + 1 x + 2 (d) lim x 0 tan( 2 x ) x (e) lim x 1 sin x 3 - 1 x - 1 (f) lim x 0 tan( 2 x ) | x | (III): Consider the following function f ( x ) = A, x is rational x 2 + 4 x, x is irrational.
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Unformatted text preview: (a) What value of A , if any, makes this functions continuous at x = 2? (b) For which value of A is this functions continuous at exactly one point? (IV): Consider the sequences given recursively by a n +1 = 1 + a n 2 and a 1 = 1 and b n +1 = 1-b 3 n and b 1 = 1 (a) Is { a n } Bounded? Monotone? Convergent? Justify your answers. (b) Is { b n } Bounded? Monotone? Convergent? Justify your answers. (c) If either sequence is convergent, compute the limit....
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