# Thread: Very basic limit help required!

1. ## Very basic limit help required!

Ok, so i was learning about limits and came across this questions

Find:

Lim
h-->0

4x^2 X h^2 + xh + h
/ (divided by)
h

So I cancelled it down to 4x^2h + x

Then I made h = 0 and that got rid of the 4x^2h and left the x

so the answer I got was x

but the book says the answer is x + 1

did I make an error? Can anyone offer assistance?

Thanks a lot... PS I'm new here so hi all

2. Originally Posted by calculusstruggler
Ok, so i was learning about limits and came across this questions

$\displaystyle \mbox{Find }\, \lim_{h\rightarrow 0}\, \frac{4x^2 h^2\, +\, xh\, +\, h}{h}$

So I cancelled it down to 4x^2h + x
Um... no....

You can only cancel factors, not terms or parts of terms. To learn how to simplify rational expressions, try here.

Then I made h = 0 and that got rid of the 4x^2h and left the x

Try using one of the techniques they showed you in your book and / or in your classroom lecture: noting that the numerator does not factor, instead divide everything by h:

. . . . .$\displaystyle \left(\frac{4x^2 h^2\, +\, xh\, +\, h}{h}\right)\left(\frac{\frac{1}{h}}{\frac{1}{h}}\ right)$

. . . . .$\displaystyle \frac{\frac{4x^2 h^2}{h}\, +\, \frac{xh}{h}\, +\, \frac{h}{h}}{\frac{h}{h}}$

. . . . .$\displaystyle \frac{4x^2 h\, +\, x\, +\, 1}{1}$

. . . . .$\displaystyle 4x^2 h\, +\, x\, +\, 1$

Now there is no "division by zero" problem, so you can simply evaluate at h = 0, thus confirming the book's answer.

3. Originally Posted by calculusstruggler
Ok, so i was learning about limits and came across this questions

Find:

Lim
h-->0

4x^2 X h^2 + xh + h
/ (divided by)
h

So I cancelled it down to 4x^2h + x

Then I made h = 0 and that got rid of the 4x^2h and left the x

so the answer I got was x

but the book says the answer is x + 1

did I make an error? Can anyone offer assistance?

Thanks a lot... PS I'm new here so hi all
shouldnt you get 4hx^2 + x + 1?? then setting h to zero would give you x+1

$\displaystyle \tfrac {4x^2h^2 + xh + h}{h} = \tfrac {4x^2h^2}{h} + \tfrac {xh}{h} + \tfrac {h}{h} = 4hx^2 + x + 1$

4. ahh thanks guys, I see what I did wrong. I simply cancelled out the h when I divided it by h, but should have made it 1 because h/h = 1 not 0

Thanks a lot for clearing that up.
Stupid stupid error, can't make those in the exam!