What is the value of the limit lim(x->0) (sin(x)/x)?

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Question: What is the value of the limit lim(x->0) (sin(x)/x)?

Options:

Correct Answer: 1

Solution:

The limit lim(x->0) (sin(x)/x) = 1.

What is the value of the limit lim(x->0) (sin(x)/x)?

What is the value of the limit lim(x->0) (sin(x)/x)?

Step 1: Understand what a limit is. A limit tells us what value a function approaches as the input gets closer to a certain point.
Step 2: Identify the function we are looking at, which is sin(x)/x.
Step 3: We want to find out what happens to sin(x)/x as x gets closer to 0.
Step 4: Directly substituting x = 0 into sin(x)/x gives us 0/0, which is undefined. So we need another method.
Step 5: Use the squeeze theorem or known limit properties. It is a known fact that as x approaches 0, sin(x)/x approaches 1.
Step 6: Therefore, we conclude that lim(x->0) (sin(x)/x) = 1.

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