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\lim _{x \rightarrow \infty} \frac{-15 x}{4+2 x}=

Jan 29, 2024

\lim _{x \rightarrow \infty} \frac{-15 x}{4+2 x}=

Solution by Steps

step 1

To find the limit of the function as

x

approaches infinity, we can divide the numerator and the denominator by the highest power of

x

in the denominator

step 2

Dividing both the numerator and the denominator by

x

, we get

\lim_{x \to \infty} \frac{-15}{\frac{4}{x}+2}

step 3

x

approaches infinity,

\frac{4}{x}

approaches 0, so the expression simplifies to

\lim_{x \to \infty} \frac{-15}{2}

step 4

The limit is therefore

-\frac{15}{2}

Answer

-\frac{15}{2}

Key Concept

Limits at Infinity of Rational Functions

Explanation

When finding the limit at infinity of a rational function, divide by the highest power of

x

in the denominator and simplify. Terms with

x

in the denominator approach 0 as

x

approaches infinity.