Provide an appropriate response.Which of the following statements describes a way to verify that L is the left-hand limit of a function f(x) at x = x0 ?I. Given ? > 0, find an interval I = ( x0-?, x0+?), ? > 0, such that if x lies in I, then  < ?.II. Given ? > 0, find an interval I = ( x0, x0+?), ? > 0, such that if x lies in I, then  < ?. III. Given ? > 0, find an interval I = ( x0-?, x0), ? > 0, such that if x lies in I, then  <

?.

A. I only
B. II only
C. III only
D. None


Answer: C

Mathematics

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Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1.3loga q - loga r + loga f - 5loga p

A. loga (3q - r + f - 5p)
B. loga  
C. loga 
D. loga  

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Find the exact solutions to the quadratic equation, using a method of your choice.0.1x2 - 0.2x - 0.1 = 0

A. 1 + 
B. 2 ± 
C. 1 ± 
D. 2 - 

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A minor arc, AB , in circle O with radius r

(a) is shorter than a semicircle in circle O. (b) has measure less than 180°. (c) has measure ?r. (d) Both (a) and (b) are true. (e) None of these is correct.

Mathematics

Calculate.Enter just a reduced fraction of form .

Fill in the blank(s) with the appropriate word(s).

Mathematics