Calculous limit problems 1

Question

i need help with problems 28 and 29. please include all work in the answers. here is a pic of the problems

http://imgur.com/KqTus5c

thanks in advance

Answer 1

Wow, hard to do without something real to write on.  I'll summarize the steps, and hopefully you can follow.

 

• For 28
• Multiply by the conjugate of the root x-3, or (rootx+3)
• Note that this gives x-9 on the bottom
• Do NOT multiply through on the top, but rather note that 9-x and x-9 are off just by a factor of -1
• Cancel the 9-x piece, and you are left with -rootx-3
• Plug in 9 at this point, and get -root9-3, or -3-3 or -6
• Limit is -6
• For 29
• FACTOR both the numerator and the denominator
• This leaves [(x+4)(x+1)]/[(x+1)(x+1)]
• Cancel the x+1 piece to leave (x+4)/(x+1)
• Now you could try to plug in -1, but since you still have division by 0, this problem has no limit.