calculus

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What is the limit of the function as x approaches infinity?
4x^4 - 4^x
Would the limit be positive infinity or negative infinity?

  • calculus -

    exponentials grow much faster than powers. note that the slope of x^4 = 4x^3 (a lower power), while the slope of 4^x is basically 4^x still.

    For example, 10^4 = 10000 but 4^10 =~ 1,000,000

    and it gets worse the farther out you go.

    So, since you're subtracting a huge number from a smaller number, the limit is -oo.

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