Question

Use the limit theorem and the properties of limits to find the limit.

Answer 1

Answer:

b. ∞

Step-by-step explanation:

Given:

$\lim_{x \to \infty} (\frac{-7x^3 + 4x + 1}{-7x^2 -9x + 3})$

Here the highest degree of the denominator polynomial is 2. Therefore, divide both the numerator and the denominator by x^2, we get

$\lim_{x \to \infty} \frac{(-7x +4/x +1/x^2}{-7 -9/x + 3/x^2} )$

When we apply limit x -->∞, the numerator become -∞ and the denominator is -7.

Note: 1/∞ = 0

Therefore, we get

= (-∞ / -7)

= ∞            [Using the sign rule and dividing infinity by anything is infinity]

Answer: b. ∞

Hope this will helpful.

Thank you.

Answer 2

Answer:

Option B. ∞ is the correct option.

Step-by-step explanation:

In this question the given expression for which we have to find the limit.

$\lim_{x\rightarrow \ \oe }\frac{-7x^{3}+4x+1}{-7x^{2}-9x+3}$

Now we will convert the expression as below

$=\lim_{x\rightarrow \ \oe }\frac{-7+\frac{4}{x^{2}}+\frac{1}{x^{3}}}{-\frac{7}{x}-\frac{9}{x^{2}}+\frac{3}{x^{3}}}$

We have done this because we know $\lim_{x\rightarrow \ \oe }\frac{1}{x}=0$

As we find the denominator as 0 therefore the limit of the given expression is ∞.