# Calc 2

posted by .

What is the lim of the square root of x times sin of (1/x) as x approaches infinity

• Calc 2 -

x^.5 * sin (1/x)
as 1/x ---> 0 , sin (1/x) = 1/x

x^.5 * x^-1 = x^-.5 = 1/sqrt x
which = 0 as x ---> infinity

• Calc 2 -

or, by this time you have probably seen L'Hospital's Rule, so

limit √x sin(1/x)
if u = 1/x, then we have
limit sin(u)/√u
= limit cos(u)/(1/2√u)
= limit 2√u cos(u) as u->0
= 0

## Similar Questions

1. ### calculus

Help - I have three problems that I am stuck on - 1. Lim x approaches infinity (x-3/x squared + 4) 2. Lim x approaches 3 x cubed - x squared - 7 x +3/ x squared - 9 3. Lim x approaches negative infinity (x + square root x squared + …
2. ### Calculus

Does the series (1+sin(n))/(10^n) from summation 0 to positive infinity converge or diverge?
3. ### calc bc (condensed

is the limit as x approaches 0 of sin3x over 3x equal to zero?
4. ### Calc. Limits

Are these correct? lim x->0 (x)/(sqrt(x^2+4) - 2) I get 4/0= +/- infinity so lim x->0+ = + infinity?
5. ### calc

Are these correct? lim x->0 (x)/(sqrt(x^2+4) - 2) I get 4/0= +/- infinity so lim x->0+ = + infinity?

Are these correct? lim x->0 (x)/(sqrt(x^2+4) - 2) I get 4/0= +/- infinity so lim x->0+ = + infinity?
7. ### Calculus

Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x>0... Should i use the formula e= lim as x->0 (1+x)^(1/x) or e= lim as x->infinity (1+1/n)^n Am i able to substitute in x/n for x?
8. ### Calculus

Find the following limit if it exists, or explain why it does not exist: lim as x approaches -infinity of square root of (9x^6-x^2) divided by x^3+5
9. ### Calc Help :(((((

lim x-> infinity (7x^(5/3)-2x^(1/3)+6)/(-2x^(8/5)-5x+square root(x))
10. ### Math

Which describes the end behavior of the graph of the function f(x)=-2x^3-5x^2+x?

More Similar Questions