Find Value of k for Limit: x^3-6 / x^k+3

  • Thread starter Thread starter starchild75
  • Start date Start date
  • Tags Tags
    Limit Value
starchild75
Messages
100
Reaction score
1

Homework Statement



find the value of k such that the limit exists. lim xgoes to infinity (x^3-6)/(x^k+3).


Homework Equations





The Attempt at a Solution



I multiply both sides by 1/x^3 I get 1 in the numerator and x^k/x^3 in the denominator. I don't know what to next.
 
Physics news on Phys.org
x^k/x^3 is x^(k-3). Consider the cases of k>3, k<3 and k=3.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Proving piecewise function is k-differentiable
Replies
5
Views
2K
Finding Limits Using Properties - Simplifying Examples
Replies
22
Views
2K
What is true for limit of f (x,y) as (x,y)→(0,1)?
Replies
3
Views
2K
Proving limit of rational function
Replies
9
Views
1K
Calculating radius of gyration of plane figure about x-axis
Replies
5
Views
2K
Limit and Integration of ##f_n (x)##
Replies
8
Views
2K
How to calculate primitive functions on maximal intervals for periodic functions?
Replies
4
Views
2K
Spivak, Ch 5 Limits, Problems 10c: Proving limit relationship
Replies
5
Views
2K
Solution verification of ODE using Frobenius' method
Replies
3
Views
1K
Show Picard iteration diverges
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top