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Find
lim_(x rarr4)(3x)/((x-2)(x+2)).
Choose 1 answer:
(A)
(1)/(4)
(B)
(3)/(4)
(C) 1
(D) The limit doesn't exist

Find $\lim _{x \rightarrow 4} \frac{3 x}{(x-2)(x+2)}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{4}$ $\newline$ (B) $\frac{3}{4}$ $\newline$ (C) $1$ $\newline$ (D) The limit doesn't exist

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Find limits of polynomials and rational functions

Full solution

Q. Find

\lim _{x \rightarrow 4} \frac{3 x}{(x-2)(x+2)}

.

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{4}

\newline

(B)

\frac{3}{4}

\newline

(C)

1

\newline

(D) The limit doesn't exist

Identify Limit: Identify the limit that needs to be evaluated. $\newline$ We need to find the limit of the function $\frac{3x}{(x-2)(x+2)}$ as $x$ approaches $4$ .
Substitute Value: Substitute the value of $x$ into the function to see if the function is defined at that point. $\lim_{x \to 4}\frac{3x}{(x-2)(x+2)} = \frac{3\cdot 4}{(4-2)(4+2)}$
Perform Calculations: Perform the calculations to evaluate the limit. $(3 \times 4)/((4-2)(4+2)) = 12/(2 \times 6) = 12/12 = 1$
Conclude Limit: Conclude the limit based on the calculations. $\newline$ Since we were able to directly substitute $x = 4$ into the function and get a result without any indeterminate forms, the limit exists and is equal to $1$ .

More problems from Find limits of polynomials and rational functions

Question

\lim _{x \rightarrow \infty} \frac{x^{2}-4}{x+4}

\newline

1

\newline

1

\newline

-1

\newline

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(D) The limit is unbounded

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f(x)=\frac{6 x^{3}}{3 x+2}

\newline

\lim _{x \rightarrow \infty} f(x)

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What happens to the value of the expression

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(A) It increases.

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(B) It decreases.

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(C) It stays the same.

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Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE).

\newline

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\newline

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\newline

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\newline

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\newline

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Question

Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE).

\newline

\lim _{x \rightarrow \infty} \frac{\sqrt{-3 x+x^{4}}}{7+8 x^{2}+10 x}

\newline

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Question

Aditya's dog routinely eats Aditya's leftovers, which vary seasonally. As a result, his weight fluctuates throughout the year.

\newline

The dog's weight

W(t)

\mathrm{kg}

) as a function of time

t

(in days) over the course of a year can be modeled by a sinusoidal expression of the form

a \cdot \cos (b \cdot t)+d

\newline

t=0

, the start of the year, he is at his maximum weight of

9.1 \mathrm{~kg}

. One-quarter of the year later, when

t=91.25

, he is at his average weight of

8.2 \mathrm{~kg}

\newline

W(t)

\newline

t

should be in radians.

Posted 21 hours ago