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calculus

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I have a couple of questions that I'm not sure how to do!

1) Given f(x) = (x^2 - 2x + 1) for x does not equal 1 and (k) for x = 1

Determine the value of k for which f is continuous for all real x.

a) 0
b) 1
c)2
d)3
e)none of the above

i think the anser is a but i'm really not sure how to solve this.

2) The graph of y = sinx / x has

I. a vertical asymptote at x=0
II. a horizontal asymptote at y=0
III. an infinite number of zeros

a) I only
b) II only
c) III only
d) I and II only
e) II and III only

I think the answer is d but I'm not positive.

If someone could please help me that would be greatly appreciated! :)

  • calculus -

    you are right on #2
    as x gets larger, you are dividing by an increasingly larger number, so the result goes to zero
    also sin(x) fluctuates between +1 and -1 so crosses the x-axis again and again.

    #1 ?
    are you sure you typed the function correctly?
    The way you have it, it is simply a parabola, which would be continuous for every x.
    Where does the k come in?
    The question is quite confusing.

  • calculus -

    Haha I know! I did type it in right... It really is confusing because I don't have a clue what to do with the k!

    But thank you for your help on question #2!! :)

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