Question

Determine whether the given limit leads to a determinate or indeterminate form. HINT [See Example 2.]

Answer 1

Answer:

The limit leads to a determinate form.

$\lim_{x \to \infty} \frac{2}{-x+3} = 0$

Step-by-step explanation:

The following are indeterminate forms.

$\frac{0}{0} \ and \ \frac{\infty}{\infty}$

Given the limit of a function $\lim_{x \to \infty} \frac{2}{-x+3}$, to show if the given limit is determinate or indeterminate form, we will need to substitute the value of -$\infty$ into the function as shown,

$\lim_{x \to \infty} \frac{2}{-x+3}\\= \frac{2}{-(-\infty)+3}\\= \frac{2}{\infty+3}\\= \frac{2}{\infty}\\\\Generally, \ \frac{a}{\infty} =0$

where a is any constant, therefore $\frac{2}{\infty} = 0$

Since we are able to get a finite value i.e 0, this shows that the limit does exist and leads to a determinate form