Thread: help would be very much appreciated please

Evaluate the limit and indicate appropriate limit laws.

lim square root of u^4+3u+6
u->-2

Evaluate the limit

lim x^2+5x+4/x^2-3x-4
x->-4

Find the limit

lim t^2+2/t^3+t^2-1
t->-infinity

Please can someone help me?

Originally Posted by bballj228

Evaluate the limit and indicate appropriate limit laws.

lim square root of u^4+3u+6
u->-2

Evaluate the limit

lim x^2+5x+4/x^2-3x-4
x->-4

Find the limit

lim t^2+2/t^3+t^2-1
t->-infinity

Please can someone help me?

For the first one all you need to know is this
Let be a function defined at some point a, then



For the second one, consider two polynomials

and if



Both and contain the factor

Now for your last one Consider multiplying by

from there you can apply the first rule I gave you remembering the lax expression where a is a nondescript constant

Hi!bballj228
here is the solution
1))A=Lt [u^4+3u+6]^1/2
u->-2
put u =-2 and u will get
A=[16]^(1/2)
if u roughly look at the xpression or its graph u will find that the xpression>0 for all values of u.
therefor A=[16]^(1/2)=+4.
2)) B=Lt (x^2+5x+4)/(x^2-3x-4) x->-4
Nox just put x=-4 u will get
B=0/24=0
3))C=Lt[t^2+2]/t^3+t^2-1
t->infinity
divide numerator and denominator by t^2 u will get
C=Lt[1+2/(t^2)]/[t+1-1/(t^2)]
t->infinity
now put t=infinity
[remember 1/infinity=0]
finally u will get
C=1/(1+infinity) = 0
(infinity+1=infinity itself)
hope this helps ya.