The answer to lim _{x rightarrow 0} frac{sin (4 x)}{x} is

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Step:1 ：The given limit is of the form lim _{x rightarrow 0} frac{sin (4 x)}{x}Step:2 ：The limit of the form frac{sin(x)}{x} as x approaches 0 is 1Step:3 ：We have a similar form but with 4x instead of xStep:4 ：We can use the property of limits that says the limit of a function times a constant is the constant times the limit of the functionStep:5 ：So, we can take the 4 out of the sine function and multiply it with the limitStep:6 ：The limit then becomes 4 times lim _{x rightarrow 0} frac{sin (x)}{x}Step:7 ：Substituting the limit value, we get 4 times 1Step:8 ：Final Answer: The answer to lim _{x rightarrow 0} frac{sin (4 x)}{x} is (boxed{4})

Answer

Step: 1 ：The given limit is of the form lim _{x rightarrow 0} frac{sin (4 x)}{x}Step: 2 ：The limit of the form frac{sin(x)}{x} as x approaches 0 is 1Step: 3 ：We have a similar form but with 4x instead of xStep: 4 ：We can use the property of limits that says the limit of a function times a constant is the constant times the limit of the functionStep: 5 ：So, we can take the 4 out of the sine function and multiply it with the limitStep: 6 ：The limit then becomes 4 times lim _{x rightarrow 0} frac{sin (x)}{x}Step: 7 ：Substituting the limit value, we get 4 times 1Step: 8 ：Final Answer: The answer to lim _{x rightarrow 0} frac{sin (4 x)}{x} is (boxed{4})

The answer to $lim_{x \to 0} \frac{\sin (4 x)}{x}$ is

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The answer to $lim_{x \to 0} \frac{\sin (4 x)}{x}$ is