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Limits And Oscillating Behavior

 Is the sentence true or false?

(1+x)(2+x)\frac{\left(1+x\right)}{\left(2+x\right)} does not exist due to oscillating behavior.

  Is the sentence true or false?

Sin(1/x) does not exist due to oscillating behavior.

Is the sentence true or false?

2 cos(1/x) does not exist due to oscillating behavior.

 Is the sentence true or false?

does not exist due to unbounded behaviour.

 Evaluate.

1/(1-x) =

Is the sentence true or false?

 cos(1/(1-x)) does not exist due to unbounded behaviour.

 Is the sentence true or false?

 (1+x)(1x)\frac{\left(1+x\right)}{\left(1-x\right)} does not exist due to oscillating behavior.

 Is the sentence true or false?

sinlimx3sin(13x)\sin\lim_{x\to3}\sin\left(\frac{1}{3-x}\right)

does not exist due to oscillating behavior

Evaluate. Cos(1/x)=

Evaluate. Sin(1/x)=