How do you find the Limit of #ln(x) / sqrtx # as x approaches infinity?
Hence the limit is
Quick answer
graph{(y-e^x)(y-x^2) = 0 [-39.96, 40.04, -164.4, 235.6]}
graph{(y - ln x)(y - x^(1/2)) = 0 [-96.4, 100.36, -4.56, 5.44]}
Hence:
By signing up, you agree to our Terms of Service and Privacy Policy
To find the limit of ln(x) / sqrt(x) as x approaches infinity, we can use L'Hôpital's rule. By applying this rule, we differentiate the numerator and denominator separately and then take the limit as x approaches infinity again.
Differentiating ln(x) with respect to x gives 1/x, and differentiating sqrt(x) with respect to x gives 1/(2*sqrt(x)).
Taking the limit as x approaches infinity of the differentiated numerator and denominator, we get:
lim(x→∞) [1/x] / [1/(2*sqrt(x))]
Simplifying this expression, we can multiply the numerator and denominator by 2*sqrt(x):
lim(x→∞) [2*sqrt(x)] / x
Now, we can cancel out the x in the denominator:
lim(x→∞) 2 / sqrt(x)
As x approaches infinity, the square root of x also approaches infinity. Therefore, the limit becomes:
lim(x→∞) 2 / ∞ = 0
By signing up, you agree to our Terms of Service and Privacy Policy
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.
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.
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.
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.
- How do you evaluate the limit #3x^2(2x-1)# as x approaches #-1/2#?
- How do you evaluate the limit #-2s^2+8s-8# as s approaches #2#?
- How do you prove that the limit of #5 - 2x= 1# as x approaches 2 using the epsilon delta proof?
- How do you prove by definition that the function #f(x)= x^2 sin (1/x)# is continuous at x=0?
- How do you find the limit of #x^sqrtx# as x approaches 0 using l'hospital's rule?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7