Calculus Archive: Questions from February 11, 2023
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4) \( \iint_{R}^{R} \frac{\ln y}{y} d A, R:\left\{(x, y) \mid 0 \leqslant x \leqslant \pi, e^{2 x} \leqslant y \leqslant e^{\cos x}\right. \)2 answers -
Questions 16,30,48
9-61. Trigonometric integrals Evaluate the following integrals. 9. \( \int \cos ^{3} x d x \) 10. \( \int \sin ^{3} x d x \) 11. \( \int \sin ^{2} 3 x d x \) 12. \( \int \cos ^{4} 2 \theta d \theta \)2 answers -
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\( \begin{aligned} \mathbf{a} & =9 \mathbf{i}-8 \mathbf{j}+7 \mathbf{k}, \quad \mathbf{b}=7 \mathbf{i}-9 \mathbf{k} \\ \mathbf{a}+\mathbf{b} & = \\ 9 \mathbf{a}+7 \mathbf{b} & = \\ |\mathbf{a}| & = \\2 answers -
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en el trigulo recangulo, su hipotenusa vale 15cm y cateto 9cm. determine la lomgitud del otro cateto2 answers
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Find the derivative. \[ \begin{array}{l} y=\frac{\sqrt[3]{x^{2}+3}}{x} \\ y^{\prime}=\frac{-3}{x^{2}\left(x^{2}+3\right)^{2 / 3}} \\ y^{\prime}=\frac{3}{x^{2}\left(x^{2}+3\right)^{2 / 3}} \\ y^{\prime2 answers -
Solve the following boundary-value problem: \( y^{\prime \prime}+9 y=0, ; y(0)=-1, y\left(\frac{\pi}{6}\right)=1 \) (A) \( y=\cos 3 x+\sin 3 x \) (B) \( y=-\cos 3 x+\sin 3 x \) (C) \( y=\cos 3 x-\sin2 answers -
Given , find = = =
Given \( f(x, y, z)=\sqrt{5 x^{2}+4 y^{2}+6 z^{2}} \) \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
Given , find = = =
Given \( f(x, y)=2 x^{3}-2 x y^{4} \) \( f_{x x}(x, y)= \) \( f_{x y}(x, y)= \) \( f_{y y}(x, y)= \)2 answers -
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can someone help me
Given \( f(x, y, z)=\sqrt{x^{2}+3 y^{2}+5 z^{2}} \), find \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
Evaluate the definite integral. \[ \int_{0}^{\pi / 3}[(\sec t \tan t) \mathbf{i}+(\tan t) \mathbf{j}+(2 \sin t \cos t) \mathbf{k}] d t \]2 answers -
just the wrong ones
Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( E \) is the solid bounded by \( z=0, x=0, z=y-6 x \) and \( y=12 \). 1. \( \int_{a}^{b} \in2 answers -
3.[9] Find the following integrals: (a) \( \int \csc ^{5} \theta \cos ^{3} \theta d \theta \) (b) \( \int_{0}^{\pi / 4} \sec ^{6} \theta \tan ^{6} \theta d \theta \) (c) \( \int \sin 2 \theta \sin 6 \2 answers -
Differentrate: 1) \( y=\sec (\theta) \tan (\theta) \) \( y^{\prime}= \) 2) \( \begin{aligned} y & =4 \sec (x)-\csc (x) \\ y^{\prime} & =\end{aligned} \) 3) \( \quad f(x)=e^{x} \sin (x)+\cos (x) \) \(2 answers -
\( -42 \) Find \( d^{2} y / d x^{2} \) (a) \( y=7 x^{3}-5 x^{2}+x \) \( y=12 x^{2}-2 x+3 \) \( y=\frac{x+1}{x} \) \( y=\left(5 x^{2}-3\right)\left(7 x^{3}+x\right) \)2 answers -
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\( \begin{array}{l}y=\sec (0) \tan (0) \\ y^{\prime}= \\ y=4 \sec (x)-\csc (x) \\ y^{\prime}= \\ f(x)=e^{x} \sin (x)+\cos (x) \\ f^{\prime}(x)= \\ f^{\prime}(x)=\frac{\cot (x)}{e^{x}} \\ f^{\prime}(x)2 answers