evaluate limit, as u -> -2, of sqrt u^4 + 3u + 6

[bballj228]

1: Evaluate the limit and indicate appropriate limit laws.

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

i know that i should Let f(x) be a function defined at some point a but i really have no clue what to do afterwards

2: Evaluate the limit

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

i know they are two polynomials

3: Find the limit

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

for this i tried multiplying by 1/x^2/1/x^2 but im not sure about the rest Please can someone help me? help would be very much appreciated!

 

[stapel]

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

Is the term above any of the following?

. . . . .\(\displaystyle \sqrt{u^4}\, +\, 3u\, + 6\)

. . . . .\(\displaystyle \sqrt{u^4\, +\, 3u}\, +\, 6\)

. . . . .\(\displaystyle \sqrt{u^4\, +\, 3u\, +\, 6}\)

Or something else?

i know that i should Let f(x) be a function defined at some point a....

I'm sorry, but I don't know what you mean by this...? Was this in the instructions, but you forgot to include it...?

2: Evaluate the limit
lim x^2+5x+4/x^2-3x-4
x->-4

Does the above mean any of the following?

. . . . .\(\displaystyle x^2\, +\, 5x\, \frac{4}{x^2}\, -\, 3x\, -\, 4\)

. . . . .\(\displaystyle \frac{x^2\, +\, 5x\, +\, 4}{x^2}\, -\, 3x\, -\, 4\)

. . . . .\(\displaystyle x^2\, +\, 5x\, +\, \frac{4}{x^2\, -\, 3x\, -4}\)

. . . . .\(\displaystyle \frac{x^2\, +\, 5x\, +\, 4}{x^2\, -\, 3x\, -\, 4}\)

Or something else?

What did you do, after you'd factored and simplified?

3: Find the limit
lim t^2+2/t^3+t^2-1
t->-infinity

Lacking grouping symbols, this one can be interpreted no better than in (2). Please reply with clarification, using the formatting explained in the articles whose links you noted when you first read the "Read Before Posting" thread.

When you reply, please include a clear listing of your work and reasoning so far. Thank you!

Eliz.

 

[galactus]

\(\displaystyle \lim_{u\to -2}\sqrt{u^{4}+3u+6}\)

This is very straightforward. Just sub in u=-2

2: Evaluate the limit

\(\displaystyle \lim_{x\to -4}\frac{x^{2}+5x+4}{x^{2}-3x-4}\)

Same as above. Just sub in x=-4

3: Find the limit

\(\displaystyle \lim_{t\to{-\infty}}\frac{t^{2}+2}{t^{3}+t^{2}-1}\)

for this i tried multiplying by 1/x^2/1/x^2 but im not sure about the rest Please can someone help me? help would be very much appreciated!

For this one, note that the power of the denominator is larger than the power of the numerator. What does that tell you. In rational expressions when you using infinity, you can disregard all but the highest powers. So, you essentially have \(\displaystyle \lim_{t\to{-\infty}}\frac{t^{2}}{t^{3}}\)

 

[bballj228]

hey thanks for the help guys, was really easier than i thought. next time i will try to make it more clear and use the correct symbols. i understand what to do now.