# For all #x>=0# and #4x-9<=f(x)<=x^2-4x+7# how do you find the limit of f(x) as #x->4?

Use the squeeze theorem.

This comes from James Stewart's Calculus section 1.6 exercises.

The last theorem of section 1.6 is the Squeeze Theorem. Use that. (In other textbooks it is also called the Pinch Theorem, and the Sandwich Theorem.)

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

To find the limit of f(x) as x approaches 4, we need to evaluate the function f(x) at x = 4. By substituting x = 4 into the given inequality, we can determine the range of f(x) near x = 4.

For x = 4, the inequality becomes 4(4) - 9 ≤ f(4) ≤ 4^2 - 4(4) + 7. Simplifying this, we get -5 ≤ f(4) ≤ 7.

Therefore, the limit of f(x) as x approaches 4 is between -5 and 7, inclusive.

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.

- How do you find the limit of #((sqrt(169-x^2))+12)/(x-5)# as x approaches 5?
- What is the limit of #(1 + sqrt3(x))(4 - 2 x^2 + x^3) # as x approaches 8?
- How do you find the limit of #x^sqrtx# as x approaches 0?
- How do you determine one sided limits numerically?
- How do you show that the function #f(x)=1-sqrt(1-x^2)# is continuous on the interval [-1,1]?

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