Calculus Archive: Questions from August 16, 2022
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Given \( f(x, y)=5 x^{2}+6 x y^{3}-6 y^{4} \) \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \end{array} \]1 answer -
5. (10 POINTS) Evaluate the integral \[ \int\left(\frac{1}{x^{2} \sqrt{x^{2}-25}}+\tan ^{-1}(\sin x) \cos x\right) d x . \]1 answer -
1.(a), (b), (d)
1. Find the general solutions to the following differential equations. (a) \( y^{\prime \prime}-y^{\prime}-6 y=0 \) (b) \( y^{\prime \prime}-6 y^{\prime}+9 y=0 \) (c) \( y=y^{\prime \prime} \) (d) \(1 answer -
2.(a), (d), (e)
2. Solve the initial value problems. (a) \( y^{\prime \prime}-5 y^{\prime}+6 y=0, \quad y(0)=1, \quad y^{\prime}(0)=1 \) (b) \( y^{\prime \prime}-2 y^{\prime}+2 y=0, \quad y(0)=-1, \quad y^{\prime}(0)1 answer -
1.(b), (c), (d)
1. Find the area of the region enclosed by the given curves. (a) \( y=x^{2}, y=2 x-x^{2} \) (b) \( x=y^{4}, y=\sqrt{2-x}, y=0 \) (c) \( y=1 / x^{2}, y=x, y=x / 8 \) (d) \( 4 x=4 y-y^{2}, 4 x-y=0 \) (e1 answer -
(iii) Evaluate the integral \( \iint_{D}\left(3 x^{2}+y^{2}\right) d A \) where \( =\left\{(x, y) \mid-2 \leq y \leq 3, y^{2}-3 \leq x \leq y+3\right\} \). Solution:1 answer -
Calcullus 3
7. Evałüe \( \int_{0}^{\infty} \mathbf{r}(t) d t \). a) \( \frac{\pi^{2}}{9} k \) b) \( \frac{2}{3} i+\frac{\pi^{2}}{9} k \) c) \( \frac{\pi^{2}+3}{9} \) d) \( \frac{1}{3} i+\frac{\pi^{2}}{9} k \) e1 answer -
Objective: tangent to a curve and to apply the derivative function to different functions. (Goals 5 and This activity is intended to help the student determine the equation of a line 6) Work on the fo
Trabaje los siguientes ejercicios presentando todo el proceso en un documentpoo en word. Valor 20 puntos. Tiene 2 intentos para adjuntar los ejercicios al curso para ser evaluados. Su 2 do intento pue1 answer -
1 answer
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Write the sum without sigma notation and evaluate it. \[ \sum_{k=1}^{4} 2 \sin \frac{\pi}{k} \] \( 2 \sin \pi+2 \sin \frac{\pi}{2}+2 \sin \frac{\pi}{3}+2 \sin \frac{\pi}{4}=1+\frac{\sqrt{3}+\sqrt{2}}{1 answer -
1 answer
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En esta actividad usted contestará los ejercicios de práctica que se presentan a continuación. Es necesario que muestre su procedimiento claro y completo para que obtenga crédito parcial o total.1 answer -
1 answer
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1 answer
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\[ \iint_{R} \frac{x y^{2}}{x^{2}+1} d A=? \] Where \( R=\{(x, y) \mid 0 \leq x \leq 1,-3 \leq y \leq 3\} \).1 answer -
1 answer
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2.(d)
2. Solve the initial value problems. (a) \( y^{\prime \prime}-5 y^{\prime}+6 y=0, \quad y(0)=1, \quad y^{\prime}(0)=1 \) (b) \( y^{\prime \prime}-2 y^{\prime}+2 y=0, \quad y(0)=-1, \quad y^{\prime}(0)1 answer