What's the limit of ((2x + 3)/x) when x tends to infinity?

Given Function Simplification: We are given the function (2x + 3)/x and we want to find the limit as x approaches infinity. To do this, we can divide each term in the numerator by x to simplify the expression.Divide by x: Divide each term in the numerator by x: (2x + 3)/x = (2x/x) + (3/x) = 2 + (3/x).Limit of Individual Terms: Now, we consider the limit of each term separately as x approaches infinity: lim_(x -> ∞) 2 = 2, since 2 is a constant and its limit is itself. lim_(x -> ∞) (3/x) = 0, because as x becomes very large, 3/x approaches 0.Combine Limits: Combine the limits of the individual terms to find the limit of the entire expression: lim_(x -> ∞) (2 + (3/x)) = lim_(x -> ∞) 2 + lim_(x -> ∞) (3/x) = 2 + 0 = 2.

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Q. What's the limit of

\left(\frac{2x + 3}{x}\right)

when

x

tends to infinity?

Given Function Simplification: We are given the function $(2x + 3)/x$ and we want to find the limit as $x$ approaches infinity. To do this, we can divide each term in the numerator by $x$ to simplify the expression.
Divide by x: Divide each term in the numerator by x: $\newline$ $(2x + 3)/x = (2x/x) + (3/x) = 2 + (3/x)$ .
Limit of Individual Terms: Now, we consider the limit of each term separately as $x$ approaches infinity: $\lim_{x \to \infty} 2 = 2$ , since $2$ is a constant and its limit is itself. $\lim_{x \to \infty} \left(\frac{3}{x}\right) = 0$ , because as $x$ becomes very large, $\frac{3}{x}$ approaches $0$ .
Combine Limits: Combine the limits of the individual terms to find the limit of the entire expression: $\lim_{x \to \infty} (2 + (3/x)) = \lim_{x \to \infty} 2 + \lim_{x \to \infty} (3/x) = 2 + 0 = 2$ .