Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number. f(x)=⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪x2+kx−23x2+4x+3x3 +202ex2−exforx<−2for−2≤x<0for x=0forx>0Let f be the function defined above, where k is a constant.(a) For what value of k, if any, is f continuous at x=−2 ? Justify your answer.

Fractions can be added and subtracted only if they're fractions. a. like b. proper c. improper d. unlike

Asequence {an} is defined recursively, with a1 = 1, a2 = 2 and, for n > 2, an = an-1 an-2 . find the term a241

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?