Find the limit \lim_{t \rightarrow \infty} \frac{t - t\sqrt t}{2t^{3/2} +3t-5}

Question:

Find the limit {eq}\lim_{t \rightarrow \infty} \frac{t - t\sqrt t}{2t^{3/2} +3t-5} {/eq}

The Limit in Calculus:

The limit of a function {eq}f(t) {/eq} can be written as: {eq}\displaystyle\lim_{x\rightarrow \, a} f(t) {/eq}

To solve this problem, we'll divide the expression by the highest denominator power in order to get a simpler form, then plug in the value of {eq}t {/eq} to get the solution.

We are given:

{eq}\lim_{t \rightarrow \infty} \frac{t - t\sqrt t}{2t^{3/2} +3t-5} {/eq}

Divide by highest denominator:

{eq}=\lim_{t \rightarrow...

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