Calculus Archive: Questions from August 10, 2023
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Find the particular solution using the initial condition. \\[ \\begin{array}{l} y^{\\prime} \\sin (2 y)-\\cos x=0, \\quad y\\left(\\frac{\\pi}{2}\\right)=0 \\\\ y=\\cos ^{-1}(-2 \\sin x+3) \\\\ y=\\fr2 answers -
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Differentiate. \\[ y=\\ln \\left[(x+4)^{2}(x+8)^{4}(x+6)^{3}\\right] \\] \\[ \\frac{d}{d x}\\left[\\ln \\left[(x+4)^{2}(x+8)^{4}(x+6)^{3}\\right]\\right]= \\]2 answers -
\\( \\lim _{(x, y) \\rightarrow(0,0)} \\frac{(x-y)\\left((\\sin x)^{2}+(\\sin y)^{2}\\right)}{x^{3}-y^{3}} \\)2 answers -
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Differentiate the function. \\[ y=\\left(5 x^{4}-x+3\\right)\\left(-x^{5}+5\\right) \\] \\[ y^{\\prime}= \\]2 answers -
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Complete the identity. \\[ \\frac{\\sin \\theta}{1+\\sin \\theta}-\\frac{\\sin \\theta}{1-\\sin \\theta}=? \\] A. \\( 1+\\cot \\theta \\) B. \\( \\sin \\theta \\tan \\theta \\) C. \\( \\sec \\theta \\4 answers -
Find \\( \\frac{d y}{d x} \\). \\[ \\begin{array}{r} \\ln y=e^{y} \\cos 3 x \\\\ \\frac{-3 y e^{y} \\sin 3 x}{1-y e^{y} \\cos 3 x} \\\\ \\frac{y e^{y} \\sin 3 x}{1-e^{y} \\cos 3 x} \\end{array} \\]2 answers -
19. Solve the initial value problem y' = e(2t - 4), y (5)=0
19. Solve the initial value problem \\[ y^{\\prime}=e^{-\\nu}(2 t-4), \\quad y(5)=0 \\]2 answers -
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\\( \\int 3 \\sin ^{3} x \\cos ^{7} x d x \\) \\( \\int 3 \\sin ^{3} x \\cos ^{7} x d x=\\frac{3}{10} \\cos ^{10} x-\\frac{3}{8} \\cos ^{8} x+C \\)2 answers -
¿Para cuál valor de \\( a \\) el siguiente conjunto de vectores es linealmente dependiente? \\[ \\{(1,-2)(6, a)\\} \\]2 answers -
Indica si el siguiente conjunto de vectores es linealmente independiente: \\[ x_{1}=(0,-3,3) \\quad x_{2}=(5,-2,-2) \\quad x_{3}=(15,-15,3) \\]2 answers -
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dy Find where y = sin dx J 2x+6)
\\( \\frac{d y}{d x} \\), where \\( y=\\sin ^{-1}\\left(\\frac{1}{9 x+6}\\right) \\).2 answers