Home > Calculus > Determining Limits Algebraically

Given #(u^4 + 3u + 6)^(1/2)# how do you find the limit as u approaches -2?

Answer 1

Cameron Alexander

Just plug it in.

#color(blue)(lim_(u->-2) (u^4 + 3u + 6)^"1/2")#

#= sqrt((-2)^4 + 3(-2) + 6)#

#= sqrt(16)#

#= color(blue)(4)#

All this means is you travel along the #u# axis and approach the value #u = -2# from either side (left/right). The answer tells you that the #v# value is #4#.

In other words, the coordinate #(u,v) = (-2, 4)# exists in #v(u) = (u^4 + 3u + 6)^"1/2"#.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Charles Anctil

To find the limit as u approaches -2 for the expression (u^4 + 3u + 6)^(1/2), we substitute -2 for u in the expression and simplify. This gives us (-2^4 + 3(-2) + 6)^(1/2), which simplifies to (16 - 6 + 6)^(1/2) = 16^(1/2) = 4. Therefore, the limit as u approaches -2 is 4.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.