How do you find the limit of #sqrt(4x^2-1) / x^2# as x approaches infinity?
Emily AmmermanIt is
#lim_(x->oo) sqrt(4x^2-1) / x^2=lim_(x->oo) [absx*sqrt(4-1/x^2)]/[x^2]= lim_(x->oo) sqrt(4-1/x^2)lim_(x->oo) 1/x=40=0#
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To find the limit of sqrt(4x^2-1) / x^2 as x approaches infinity, we can simplify the expression by dividing both the numerator and denominator by x^2. This gives us sqrt(4 - 1/x^2) / 1. As x approaches infinity, 1/x^2 approaches 0. Therefore, the expression simplifies to sqrt(4 - 0) / 1, which is equal to 2. Hence, the limit of sqrt(4x^2-1) / x^2 as x approaches infinity is 2.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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