A x + 2A + B x + B \] \[ 2x+3 = (A + B) x + (2A + B) \] Matching coefficients: \[ A + B = 2 \] \[ 2A + B = 3 \] Subtract the first from the second: \[ (2A + B) - (A + B) = 3 - 2 \Rightarrow A = 1 \] Then, \( B = 2 - A = 1 \). Rewrite integral: \[ \int \le
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= -\sin t \), \( \frac{dy}{dt} = \cos t \). Find \( \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{\cos t}{-\sin t} = -\cot t \). At \( t = \frac{\pi}{4} \): \( \cot \frac{\pi}{4} = 1 \). Therefore, \( \frac{dy}{dx} = -1 \). Answer: \( -1 \). Strategy: Use
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