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You Won’t Believe How These Grandmas Turn Pods Into Daily Magic! - Londonproperty

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 To find the horizontal asymptote of the rational function \( G(t) = \frac{3t^2 + 2t + 1}{t + 1} \), we analyze the degrees of the numerator and the denominator.

📌 The degree of the numerator is 2, and the degree of the denominator is 1. Since the degree of the numerator is greater than the degree of the denominator, the function does not have a horizontal asymptote. Instead, it has an oblique (slant) asymptote.

📌 To find the slant asymptote, perform polynomial long division of \( 3t^2 + 2t + 1 \) by \( t + 1 \):

📌 Divide \( 3t^2 \) by \( t \) to get \( 3t \).

📌 Multiply \( 3t \) by \( t + 1 \): \( 3t^2 + 3t \).

📌 Subtract: \( (3t^2 + 2t + 1) - (3t^2 + 3t) = -t + 1 \).

📌 Divide \( -t \) by \( t \) to get \(-1\).

📌 Multiply: \(-1(t + 1) = -t - 1\).

🔥 Popular Posts

Find the minimum value of this expression for $ x \in (0, \frac{\pi}{2...
We expand both terms:
\sin^2 x + \cos^2 x + \sec^2 x + \csc^2 x + 2(\tan x + \cot x)
Use identity $ \sin^2 x + \cos^2 x = 1 $, and:
+ (1 + \tan^2 x) + (1 + \cot^2 x) + 2(\tan x + \cot x) = 3 + \tan^2 x...
Let $ t = \tan x + \cot x $. Then:
\tan^2 x + \cot^2 x = t^2 - 2
+ (t^2 - 2) + 2t = t^2 + 2t + 1 = (t + 1)^2
Now, $ t = \tan x + \cot x \geq 2 $ by AM-GM, with equality when $ \ta...
So minimum occurs at $ t = 2 $, giving:

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