# How do you use the Squeeze Theorem to find #lim (1/x)cosx# as x approaches infinity?

Accordingly, at infinity, by the squeeze theorem,

By signing up, you agree to our Terms of Service and Privacy Policy

To use the Squeeze Theorem to find the limit of (1/x)cosx as x approaches infinity, we need to find two functions that "squeeze" the given function and have the same limit as x approaches infinity.

First, we can observe that -1 ≤ cosx ≤ 1 for all values of x. Therefore, we can say that -1/x ≤ (1/x)cosx ≤ 1/x.

Now, let's find the limits of the two bounding functions as x approaches infinity.

As x approaches infinity, -1/x approaches 0.

Similarly, as x approaches infinity, 1/x also approaches 0.

Therefore, by the Squeeze Theorem, since -1/x ≤ (1/x)cosx ≤ 1/x and both -1/x and 1/x approach 0 as x approaches infinity, the limit of (1/x)cosx as x approaches infinity is also 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.

- What is the limit of # (x +sqrt((x^2)+(3x)))# as x goes to infinity?
- What's the limit of #(x^n-a^n)/(x-a)# as #x# approaches #a# , using the derivate number which is #f'(a)# ?
- What is # lim_(->-oo) f(x) = (xe^x)/x^2#?
- Evaluate the limit # lim_(n rarr 0) (lamda^n-mu^n)/n# ?
- What is the limit as #x# approaches #2# for #sin(x^2 - 3x + 2)/x^2 - 2#?

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