Calculus Archive: Questions from November 07, 2022
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2 answers
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#10, #12 and #16 please
In Exercises 9-20, find the Hessian matrix \( f^{\prime \prime} \). 9. \( f(x, y)=\sin (x y) \) 10. \( f(x, y)=x y \) 11. \( f(x, y)=\sin x+\cos (2 y) \) 12. \( f(x, y)=x^{2}+y^{2} \) 16. \( f(x, y)=2 answers -
Find the slant asymptote of \( h(x)=\frac{3 x^{3}+11 x^{2}+16 x+9}{x^{2}+2 x+1} \) 26. A \( y=3 x \) B \( y=2 x+11 \) C \( y=11 x \) D \( y=11 x+4 \) \( \mathbf{E} \quad y=2 x+1 \) F \( y=3 x+5 \)2 answers -
2 answers
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Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ \begin{array}{r} y=\sqrt{x} \ln (x) \\ y^{\prime}=\frac{\ln (x)+2}{2 \sqrt{x}} \end{array} \]2 answers -
2 answers
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\[ \left(x^{\frac{2}{3}}\right)\left(x^{\frac{3}{5}}\right) \] \( \frac{y^{\frac{4}{3}}}{y^{\frac{5}{8}}} \) \[ \frac{x^{\frac{3}{4}} y^{\frac{1}{5}}}{x^{3} y^{\frac{2}{3}}} \] \[ e^{5 x} e^{3 x} \]2 answers -
2 answers
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2 answers
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find maximums and minimums, critical points, saddle points, tipe 1 or type 2? thank you
1. Determine la rotación en el punto \( A \) de la barra que se muestra en la figura. Solo debe establecer las ecuaciones. No tiene que resolver las integrales. 2. Determine el módulo en cortante si0 answers -
Find the gradient vector field \( (\vec{F}(x, y, z)) \) of \( f(x, y, z)=\ln (2 x+4 y+z) \). \[ \vec{F}(x, y, z)=\langle \]2 answers -
Find the gradient vector field \( (\vec{F}(x, y, z)) \) of \( f(x, y, z)=x^{2} y^{4} z^{5} \). \[ \vec{F}(x, y, z)=\langle \]2 answers -
Find the gradient vector field \( (\vec{F}(x, y, z)) \) of \( f(x, y, z)=e^{3 x+5 y+8 z} \) \[ \vec{F}(x, y, z)=\langle \]2 answers -
Find the gradient vector field \( (\vec{F}(x, y, z)) \) of \( f(x, y, z)=\tan (6 x+3 y+z) \). \[ \vec{F}(x, y, z)=\langle \]2 answers -
Find the gradient vector field \( (\vec{F}(x, y, z)) \) of \( f(x, y, z)=\sqrt{2 x^{2}+4 y^{2}+5 z^{2}} \) \( \vec{F}(x, y, z)=\langle \)2 answers -
Find the gradient vector field \( (\vec{F}(x, y, z)) \) of \( f(x, y, z)=z e^{-3 y x} \). \[ \vec{F}(x, y, z)=\langle \]2 answers -
Which of the following integrals is (are) equal to \( \int_{0}^{3} \int_{0}^{4 x} f(x, y) \mathrm{dy} \mathrm{dx} \) ? (e) \( \int_{1}^{3} \int_{0}^{4 x} f(x, y) d y d x+\int_{0}^{4} \int_{y / 4}^{1}2 answers -
2 answers
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Evaluate \( \iiint_{E}(x+y-4 z) d V \) where \( E=\left\{(x, y, z) \mid-2 \leq y \leq 0,0 \leq x \leq y, 02 answers -
Please solve all of them 49, 51, 53, 55, and 57 with steps 🙏
function. 45. \( y=\left(x^{2}+2\right)^{2}\left(x^{4}+4\right)^{4} \quad \) 46. \( y=\frac{e^{-x} \cos ^{2} x}{x^{2}+x+1} \) 47. \( y=\sqrt{\frac{x-1}{x^{4}+1}} \) 48. \( y-\sqrt{x} e^{x^{\prime}} x(2 answers -
i.) \( \int_{2}^{\infty} \frac{9}{(1-3 x)^{4}} d x \) ii.) \( \int_{1}^{\infty} \frac{1}{\sqrt[9]{w}} d w \) iii.) \( \int_{-\infty}^{-1} \frac{1}{\sqrt{2-r}} d r \) iv.) \( \int_{0}^{\infty} k e^{-51 answer -
slove all the questions 51, 53, 55 and 57 with steps PLEASE ALL OF THEM 🙏🙏
function. 45. \( y=\left(x^{2}+2\right)^{2}\left(x^{4}+4\right)^{4} \quad \) 46. \( y=\frac{e^{-x} \cos ^{2} x}{x^{2}+x+1} \) 47. \( y=\sqrt{\frac{x-1}{x^{4}+1}} \) 48. \( y-\sqrt{x} e^{x^{2}} x(x+1)^2 answers -
( 1 point) Find \( y \) as a function of \( x \) if \[ \begin{array}{l} y^{\prime \prime \prime}+64 y^{\prime}=0 \\ y(0)=8, \quad y^{\prime}(0)=8, \quad y^{\prime \prime}(0)=0 \\ y(x)= \end{array} \]2 answers -
( 1 point) Find \( y \) as a function of \( x \) if \[ \begin{array}{c} y^{\prime \prime \prime}-5 y^{\prime \prime}-y^{\prime}+5 y=0 \\ y(0)=-6, \quad y^{\prime}(0)=-4, \quad y^{\prime \prime}(0)=-302 answers -
41, 42 & 47
37. \( \sum_{k=1}^{\infty} \frac{1}{1+\sqrt{k}} \) 38. \( \sum_{k=1}^{\infty} \frac{k !}{k^{k}} \) 39. \( \sum_{k=1}^{\infty} \frac{\ln k}{e^{k}} \) 40. \( \sum_{k=1}^{\infty} \frac{k !}{e^{k^{2}}} \)2 answers -
Let \( P=\{(x, y): 1 \leq x+y \leq 4,-2 \leq x-y \leq 1\} \). Compute the value of the integral \( \iint_{P} \cos (x+y) \sin (x-y) d x d y \) using a change of variables.2 answers -
Given \( f(x, y, z)=\sqrt{4 x^{2}+6 y^{2}+2 z^{2}} \) \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
Given \( f(x, y)=-2 x^{5}-4 x y^{6} \) \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \( f_{y y}(x, y)= \)2 answers -
11 please
Using the Second Partials Test In Exercises 9-24, find all relative extrema and saddle points of the function. Use the Second Partials Test where applicable. 9. \( f(x, y)=x^{2}+y^{2}+8 x-12 y-3 \) 102 answers -
Find dy/dx and simplify your answers whenever possible. SHOW YOUR SOLUTIONS. 1. \( y=17^{9 x} \) 2. \( y=e^{x^{2}} \) 3. \( y=\sin \left(e^{3 x}\right) \) 4. \( y=\pi^{\frac{1}{x}} \) 5. \( y=\sqrt{2^2 answers -
2 answers
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2 answers
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Solve using Laplace Transform only
Solve \( y^{(4)}-y=0, y(0)=0, y^{\prime}(0)=0, y^{\prime \prime}(0)=1, y^{\prime \prime \prime}(0)=2 \).2 answers -
If \( f(x)=\int_{1}^{x^{3}} t^{3} d t \) then \( f^{\prime}(x)= \) If \( y(t)=\int_{0}^{t^{6}} \sqrt{15+x^{7}} d x \) \( y^{\prime}(t)= \)2 answers -
ntiate \( y=e^{x} \cos \left(x^{2}\right): y^{\prime}= \) \( e^{x} \cos \left(x^{2}\right)-2 x \sin \left(x^{2}\right) \) \( -2 x e^{x} \sin \left(x^{2}\right) \) \( e^{x}\left(\cos \left(x^{2}\right)2 answers -
2 answers
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Calculate the double integral. \[ \iint_{R} \frac{7\left(1+x^{2}\right)}{1+y^{2}} d A, R=\{(x, y) \mid 0 \leq x \leq 5,0 \leq y \leq 1\} \]2 answers -
Find the derivative.
\( y=6 x^{-\frac{1}{2}}+14 x^{-\frac{6}{7}} \) \( y=6 \sqrt[3]{x}+\frac{14}{\sqrt[7]{x}} \)2 answers -
2 answers
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Find the derivative.
\( y=\ln \left(2 x^{5}+3 x\right)^{\frac{8}{5}} \) \( y=\ln \left|2 x^{2}-7 x\right| \)2 answers -
Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, x=0, z=y-5 x \) and \( y=10 \). \[ \begin{arr2 answers -
(1 point) Let \( y \) be the solution of the initial value problem \[ y^{\prime \prime}+y=-\sin (2 x), y(0)=0, y^{\prime}(0)=0 . \] The maximum value of \( y \) is2 answers -
Problem7. Find the length of the curve (i) \( y=\ln \left(1-x^{2}\right), \quad 0 \leqslant x \leqslant 1 / 2 \). (ii) \( x=\frac{y^{4}}{8}+\frac{1}{4 y^{2}} \quad 1 \leqslant y \leqslant 2 \).2 answers -
2 answers
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Determine d^2y/ dx^2 if y = ((xe)^x) - (sin (x^2)) / x - in x
1. Determine \( \frac{d^{2} y}{d x^{2}} \) if \( y=\frac{x e^{x}-\sin x^{2}}{x-\ln x} \).2 answers