Calculus Questions from Dec 05,2024

Browse the Calculus Q&A Archive for Dec 05,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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(1 point) Use the Divergence Theorem to calculate the flux of \( \mathbf{F} \) across \( S \), where \( \mathbf{F}=z \boldsymbol{i}+y \boldsymbol{j}+z x \boldsymbol{k} \) and \( S \) is the surface of the tetrahedron enclosed by the coordinate planes and the plane \[ \frac{x}{3}+\frac{y}{2}+z=1 \] \( \iint_{S} \mathbf{F} \cdot d \mathbf{S}=\square \) Culcule las derivatas Ruciciles \( \frac{d f}{d x} \frac{\partial f}{d y} \frac{\partial f}{d z} \) de las siguentes foncion-s \( f(x, y)=\frac{x^{2}+4}{y-3} \) Integrate the function shown below. \[ \int \frac{x+4}{(x+10)(x-1)} d x \] Let \( f(x)=\cos (3 x) \) on the interval \( [-4,8] \). Partition the interval \( [-4,8] \) into 4 equal subintervals. Find the left and right Riemann sums, \( L_{4} \) and \( R_{4} \), respectively. You only need to type in the expression that represents the sum without calculating it, for example, \( \cos (-1) \cdot 2+\cos (1) \cdot 2+\cos (3) \cdot 2 \). \( L_{4}= \) Submit Question Question 3 Let \( f(x)=4^{x+3} \) on the interval \( [-2,10] \). Partition the interval \( [-2,10] \) into 4 equal subintervals . Find the left and right Riemann sums. You only need to type in the expression that represents the sum without calculating it, for example, \( 4^{1} \cdot 2+4^{2} \cdot 2+4^{3} \cdot 2+4^{4} \cdot 2 \). Left Riemann sum is Right Riemann sum is Submit Question Write out the form of the partial fractions using generic constants, for example, \( \frac{A_{1} x+B_{1}}{f_{1}(x)}+\frac{A_{2} x+B_{2}}{f_{2}(x)}+\cdots \), that would be used to perform the indicated integration. Do not evaluate the constants. \[ \int \frac{7+x}{x^{2}+2 x-24} d x \] Let \( f(x)=\sqrt[9]{x+7} \) on the interval \( [-5,1] \), Partition the interval \( [-5,1] \) into 3 equal subintervals . Find the left and right Riemann sums, \( L_{3} \) and \( R_{3} \), respectively. You only need to type in the expression that represents the sum without calculating it, for example, \( \sqrt[0]{1} \cdot 2+\sqrt[0]{2} \cdot 2+\sqrt[9]{3} \cdot 2+\sqrt[9]{4} \cdot 2 \). \( L_{3}=\square \) \( R_{3}=\square \) a) \( f^{\prime}(I)+g^{\prime}(I)= \) b) \( f(0)+g^{\prime}(-2)= \) Integrate the function shown below. \[ \int \frac{17-x}{x^{2}+2 x-3} d x \] 4. Dada as funções \( \mathrm{f}(\mathrm{x})=5-2 \mathrm{xeg}(\mathrm{x})=3 \mathrm{x}^{2}-1 \), determine: a) \( f^{\prime}(1)+g^{\prime}(1)= \) b) \( f(0)+g^{\prime}(-2)= \)
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