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Math Help - Find the limit for the given function.

  1. #1
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    Find the limit for the given function.

    Find the limit for the given function.

    i know that i need to divide through by x, both top and bottom, but what do i do after this?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by plstevens View Post
    Find the limit for the given function.
    note that: \frac {\sin 4x}x = \frac 44 \cdot \frac {\sin 4x}x = 4 \cdot \frac {\sin 4x}{4x}

    thus: \lim_{x \to 0} \frac {\sin 4x}x = 4 \lim_{x \to 0} \frac {\sin 4x}{4x}

    now continue

    Hint: this is in the form of a special limit


    i know that i need to divide through by x, both top and bottom, but what do i do after this?
    that would make no sense, you'd end up with exactly the same thing....
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    I'm confused i still don't know what to do
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  4. #4
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    Quote Originally Posted by plstevens View Post
    I'm confused i still don't know what to do
    Do you know that \lim_{z \rightarrow 0}\frac{\sin z}{z} = 1?

    What Jhevon has done is re-write your limit into this form (so z = 4x in this particular case).

    So the answer is (4)(1) = 4.
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  5. #5
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    which are continuous functions

    Which of the following are continuous functions? (Select all that apply.)

    The temperature at a specific location as a function of time.
    The temperature at a specific time as a function of the distance due west from New York City.
    The altitude above sea level as a function of the distance due west from New York City.
    The cost of a taxi ride as a function of the distance traveled.
    The current in the circuit for the lights in a room as a function of time.
    None of these.
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  6. #6
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    Quote Originally Posted by plstevens View Post
    Which of the following are continuous functions? (Select all that apply.)

    The temperature at a specific location as a function of time.
    The temperature at a specific time as a function of the distance due west from New York City.
    The altitude above sea level as a function of the distance due west from New York City.
    The cost of a taxi ride as a function of the distance traveled.
    The current in the circuit for the lights in a room as a function of time.
    None of these.
    Memo: Start a new thread for a new and unrelated problem. This question has been answered here.
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