Dick said:sin(4x)/(4x) isn't 1. The limit as x->0 of sin(4x)/(4x) is 1. Have you proved limit u->0 of sin(u)/u=1? Then just put 4x=u.
The Squeeze Theorem, also known as the Sandwich Theorem or the Pinching Theorem, is a mathematical theorem used to prove the limit of a function by "squeezing" it between two other functions with known limits. It is commonly used to evaluate limits involving trigonometric, exponential, and logarithmic functions.
To use the Squeeze Theorem, you must have a function that is sandwiched between two other functions with known limits. If the two surrounding functions have the same limit as each other, then the middle function must also have the same limit.
No, the Squeeze Theorem can only be used when the function is squeezed between two other functions with known limits. Additionally, the two surrounding functions must have the same limit for the theorem to be applicable.
The Squeeze Theorem is commonly used in calculus to evaluate limits involving trigonometric, exponential, and logarithmic functions. It is also used in real-world applications such as physics, engineering, and economics to model and analyze various systems.
Yes, the Squeeze Theorem can only be used to evaluate limits as x approaches a specific value. It cannot be used to evaluate limits at infinity or for limits that do not exist. Additionally, the theorem does not apply to functions that are not sandwiched between two other functions with known limits.