Question

lim (4x-x^2)/(2-sqrtx)
x->4

How is it 16?

Answer 1

factor and cancel, or multiply by the conjugate
your choice

Answer 2

Alright satellite take it away :P .

Answer 3

Try multiply by the conjugate

Answer 4

I rationalized personally.

Answer 5

i pick factoring

Answer 6

Yea.. what Satellite said

Answer 7

damn typo
\[\frac{x(4-x)}{2-\sqrt{x}}=\frac{x(2-\sqrt{x})(2+\sqrt{x})}{2-\sqrt{x}}\]

Answer 8

Was about to say :P .

Answer 9

cancel, replace \(x\) by \(16\)

Answer 10

Replace x with 4 not 16 :P .

Answer 11

Oh alright thanks a lot! Sometimes I get stuck on little things.

Answer 12

you can do what @Luigi0210 said too
try it and see
multiply top and bottom by \(2+\sqrt{x}\)
leave the numerator in factored form, cancel the \(4-x\) top and bottom

Answer 13

oh right, replace \(x\) by \(4\) not \(16\)

Answer 14

@Dido525 keeping me honest here ...

Answer 15

I try :) .

Answer 16

L'hospital's rule would work here too I think.