Question

exercise 1
a. write the following mathematical expressions or equations into verbal statements

1. \\( \lim _ { x \

ightarrow - 2 ^ { - } } \left( 2 x ^ { 2 } \
ight) \\)

1. \\( \lim _ { x \

ightarrow 1 } \left( x ^ { 2 } - 2 x + 1 \
ight) = 0 \\)

1. \\( \lim _ { x \

ightarrow 1 ^ { + } } \left( 5 x ^ { 2 } - 1 \
ight) \\)

1. \\( \lim _ { x \

ightarrow - 3 } \left( \frac { 2 x ^ { 2 } } { x + 1 } \
ight) = - 4 \\)
b. write the following verbal statements into mathematical expressions or equations

1. the limit of the sum of one and thrice of \\( x \\) as \\( x \\) approaches 2
2. the limit of absolute value of \\( x \\) as \\( x \\) approaches to 0
3. the limit of the quotient of \\( x \\) equaled minus 9 and \\( x \\) minus 3 as \\( x \\) approaches 3 is equal to 6
4. the limit of the square root of \\( x \\) minus 3 as \\( x \\) approaches 7 equals 2

exercise 2

Explanation:

Step1: Translate mathematical expressions to verbal statements

For \( \lim_{x

ightarrow - 2}(2x^{2})\)
The limit of \(2x^{2}\) as \(x\) approaches \(-2\)

For \( \lim_{x

ightarrow +\infty}(5x^{2}-1)\)
The limit of \(5x^{2}-1\) as \(x\) approaches positive infinity

For \( \lim_{x

ightarrow 1}(x^{2}-2x + 1)=0\)
The limit of \(x^{2}-2x + 1\) as \(x\) approaches \(1\) is equal to \(0\)

For \( \lim_{x

ightarrow - 3}(\frac{2x + 6}{x+3})=-4\)
The limit of \(\frac{2x + 6}{x + 3}\) as \(x\) approaches \(-3\) is equal to \(-4\)

Step2: Translate verbal statements to mathematical expressions

For "The limit of sum of one and thrice of \(x\) as \(x\) approaches \(2\)"

\(\lim_{x
ightarrow 2}(1 + 3x)\)

For "The limit of absolute value of \(x\) as \(x\) approaches \(0\)"

\(\lim_{x
ightarrow 0}|x|\)

For "The limit of the quotient of \(x\) squared minus \(9\) and \(x\) minus \(3\) as \(x\) approaches \(3\) is equal to \(6\)"

\(\lim_{x
ightarrow 3}\frac{x^{2}-9}{x - 3}=6\)

For "The limit of the square root of \(x\) minus \(3\) as \(x\) approaches \(7\) equals \(2\)"

\(\lim_{x
ightarrow 7}(\sqrt{x}-3)=2\)

Answer:

1. The limit of \(2x^{2}\) as \(x\) approaches \(-2\)
2. The limit of \(5x^{2}-1\) as \(x\) approaches positive infinity
3. The limit of \(x^{2}-2x + 1\) as \(x\) approaches \(1\) is equal to \(0\)
4. The limit of \(\frac{2x + 6}{x + 3}\) as \(x\) approaches \(-3\) is equal to \(-4\)
5. \(\lim_{x

ightarrow 2}(1 + 3x)\)

1. \(\lim_{x

ightarrow 0}|x|\)

1. \(\lim_{x

ightarrow 3}\frac{x^{2}-9}{x - 3}=6\)

1. \(\lim_{x

ightarrow 7}(\sqrt{x}-3)=2\)