True or false on certain limit "theory" questions

The following are the questions I am having trouble understanding. (The answers in the boxes are the correct answers)

"(1 pt) Enter a T or an F in each answer space below to indicate whether the corresponding statement is true or false. A statement is true only if it is true for all possibilities. You must get all of the answers correct to receive credit.

**1.** If http://gauss.vaniercollege.qc.ca/web...910e13a9c1.png is continuous at http://gauss.vaniercollege.qc.ca/web...6cc830a571.png, then http://gauss.vaniercollege.qc.ca/web...910e13a9c1.png is differentiable at http://gauss.vaniercollege.qc.ca/web...6cc830a571.png

**2.** http://gauss.vaniercollege.qc.ca/web...545475ad91.png

**3.** If http://gauss.vaniercollege.qc.ca/web...d6f9449881.png and http://gauss.vaniercollege.qc.ca/web...41e52443a1.png, then http://gauss.vaniercollege.qc.ca/web...b0e1749cb1.png does not exist

**4.** If http://gauss.vaniercollege.qc.ca/web...3c2c9b49f1.png and http://gauss.vaniercollege.qc.ca/web...41e52443a1.png, then http://gauss.vaniercollege.qc.ca/web...b0e1749cb1.png does not exist

**5.** http://gauss.vaniercollege.qc.ca/web...93d6e792b1.png"

I have the answers but I was hoping someone could at least briefly explain why each one is true or false.

Any help would be greatly appreciated!

Thanks in advance!