1)
and use the formula
2)
Let . Then as .
Then the limit is
3) Factorize the denominator:
Well, you're going to run into problems because does not equal . Remember, that the logarithim with base "a" is asking you to find the power to raise it to get "b". In this case: . Do you see what you do from there?Differentiate y = logx3 (base is x) ie. y^3 = x
If and ;Evaluate lim xsin1/x using u=1/x
x=>∞
Then we can rewrite this problem as . Now, we need to look at the equation . The limit as x approaches infinity of this equation is zero yes? Then we can say that the limit as x approaches infinity of is the same as the limit as u approaches 0 of .
Now this may not be any help if you haven't learned the squeeze theorem of haven't seen a limit of sin and x written as such.
Oh I hated these when I first started. Because they look so dastardly, but when the instructor did it - it all seemed so easy. And it is as this can be done in a few steps:lim (√x - √5)/(x-5)
x=>5
Can you take it from here?