Tugas 2 TUTON MATA4110/KALKULUS I 1. Jika y = 3x² - 2x + 5 , tentukan dy/dx dengan menggunakan definisi. 2. Diketahui f(x) = x² - 1. Tentukan: a. persamaan garis singgung; b. persamaan garis normal; dan c. gambarkan grafik garis singgung dan garis normal tersebut pada perpotongan kurva f(x) tersebut dengan garis x = -1. 3. Diketahui y = x cos 2x , Tentukan: a. y'''(x) b. y'''(?) 4. Tentukan dy/dx dari fungsi: a. y = ln(sin(x³ - 1)) [menggunakan aturan rantai turunan/derivatif]; dan b. implisit F(x, y) = 2x²y - sin xy² + e??? = 10 5. Diketahui f(x) = sin 2x . a. Tentukan ekspansi deret Taylor di sekitar x = ?/2 , sampai 5 suku saja. b. Tentukan ekspansi deret Maclaurin, sampai 4 suku saja. Catatan: Jawaban diupload di tempat Tugas bukan dikirim via email
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To find \( \frac{dy}{dx} \) using the definition, we need to use the limit definition of the derivative. The derivative of a function \( f(x) \) at a point \( x \) is defined as: \[ f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \] In this case, we have \( y = Show more…
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