More Calc help?

Question

1.) Does this limit =0? or am I wrong?
Lim sin(pi/x)
x>0
2.) Does this limit exist?
Lim xsin(1/x)
3.) Is there a number such that the limit Lim as x tends to 0 of 2x^2-3ax +x - a - 1/ x^2 - 2x - 3

Answer 1

1) Find the limit as x→0 of sin(π/x).

As x→0, sin(π/x)→sin(∞)

This does not approach a limit but oscillates back and forth between -1 and 1. There is no limit.
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You didn't say what x approaches. I assume you mean:

2) Find the limit as x→0 of xsin(1/x)

As we saw above sin(1/x) oscillates between -1 and 1 as x→0. If we multiply this by x = 0, we will get zero as a limit.
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3) Don't know what you have in mind. You are in calculus. You should know by now how to use parentheses properly to clarify.