Question

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?

Answer 1

Use the squeeze theorem.

Explanation:

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.)

`lim_(xrarr4)(4x-9) = 4(4)-9 = 16-9 = 7`

`lim_(xrarr4)(x^204x+7) = (4)^2-4(4)+7 = 16-16+7 = 7`

Therefore, by the Squeeze Theorem, `lim_(xrarr4)f(x) = 7`