Calculus Archive: Questions from November 01, 2022
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Find \( \frac{d^{2} y}{d x^{2}} \) for \[ \begin{array}{r} y=4 x^{2} \cos (x)+1 \sin (x) \\ \frac{d^{2} y}{d x^{2}}=8 x \cos (x)-4 x^{2} \sin (x)+\cos (x) \end{array} \]2 answers -
- In problems 2 to 5 find the eigenvalues and eigenfunctions for the given boundary-value problem. 2. \( y^{\prime \prime}+\lambda y=0, \quad y(0)=0, \quad y(\pi)=0 \) 3. \( y^{\prime \prime}+\lambda2 answers -
(1 point) Find \( \frac{d^{2} y}{d x^{2}} \) for \[ y=\csc (x) \] \[ \frac{d^{2} y}{d x^{2}}= \] (1 point) Let \( f(x)=\frac{5 \tan x}{x} \). Find \( f^{\prime}(x) \) Answer:2 answers -
2 answers
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\[ \int \cos ^{5} x \sin x d x \] \[ \int \cos ^{3} x \sin ^{4} x d x \] 8. \( \int \sin ^{3} x d x \) 10. \[ \int \cos ^{3} \frac{x}{3} d x \]2 answers -
14. \( \int \frac{\cos ^{3} t}{\sqrt{\sin t}} d t \) \( \int \sin ^{2} 5 x d \) 18. \[ \int x^{2} \sin ^{2} x d x \]2 answers -
Solve the differential equations with the given starting values:
iii. \( \quad y^{\prime \prime}-5 y^{\prime}+4 y=0 ; \quad y^{\prime}(0)=8 ; y(0)=5 \) iv. \( y^{\prime \prime}+4 y=0 ; \quad y^{\prime}(0)=2, y(0)=0 \) v. \( \quad y^{\prime \prime}+2 y^{\prime}+y=02 answers -
Evaluate the double integral. \[ \iint_{0} e^{-y^{2}} d A_{1} \quad D=\{(x, y) \mid 0 \leq y \leq 6,0 \leq x \leq y\} \]2 answers -
evaluate the double integral
\( \iint_{D} y^{2} e^{x y} d A, \quad D=\{(x, y) \mid 0 \leqslant y \leqslant 4,0 \leqslant x \leqslant y\} \)2 answers -
2 answers
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Find the absolute minimum value of the given function on the specified interval. \[ f(x)=x^{2}-5 x+1 ; \quad[0,2] \] A) \( y=-\frac{21}{4} \) B) \( y=-10 \) C) \( y=-5 \) D) \( y=0 \) E) \( y=1 \)2 answers -
Find the differential of each function. (a) \( y=\tan (\sqrt{5 t}) \) \( d y= \) (b) \( y=\frac{5-v^{2}}{5+v^{2}} \)2 answers -
2 answers
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2 answers
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Consider the following. \( \iint_{D} x y d A, D \) is enclosed by the curves \( y=x^{2}, y=2 x \) Express \( D \) as a region of type \( I \). \[ \begin{array}{l} D=\left\{(x, y) \mid 2 \leq x \leq 4,2 answers -
2 answers
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2 answers
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1. 2.
Find \( \iint_{R} x^{2} d A \) where \( R=\left\{(x, y) \mid 4 x^{2}+9 y^{2} \leq 36\right\} \) Find the mass of the solid bounded below by the circular cone \( z=\sqrt{x^{2}+y^{2}} \) and above by t2 answers -
Evaluate the triple integral \( \iiint_{E} f(x, y, z) d V \) over the solid \( E \). \[ f(x, y, z)=e^{\sqrt{x^{\overline{2}} \overline{+} y^{2}}}, E=\left\{(x, y, z) \mid 1 \leq x^{2}+y^{2} \leq 16, y2 answers -
Find \( \mathrm{dy} / \mathrm{dx} \) using logarithmic differentiation 4. \( \mathrm{y}=(\ln \mathrm{x})^{\sin \mathrm{x}} \) 5. \( \mathrm{y}=\frac{x^{2}\left(x^{5}-4 x\right)^{3}}{\sqrt{\cos x-\sin2 answers -
1. 2.
Evaluate \( \iiint_{E}(x+y-5 z) d V \) where \[ E=\left\{(x, y, z) \mid-2 \leq y \leq 0,0 \leq x \leq y, 03 answers -
Compute the Jacobian \( \mathrm{J}(u, v) \) for the following transformation. \( T: x=16 u \cos (\pi v), y=16 u \sin (\pi v) \) Choose the correct Jacobian determinant of T below. A. \( J(u, v)=\frac{2 answers -
2 answers
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Find \( \mathrm{dy} / \mathrm{dx} \) using logarithmic differentiation 4. \( y=(\ln x)^{\sin x} \) 5. \( \mathrm{y}=\frac{x^{2}\left(x^{5}-4 x\right)^{3}}{\sqrt{\cos x-\sin x}} \)2 answers -
2. Find \( f_{x} \) and \( f_{y} \) from the following: (a) \( f(x, y)=x^{2}+5 x y-y^{3} \) (c) \( f(x, y)=\frac{2 x-3 y}{x+y} \) (b) \( f(x, y)=\left(x^{2}-3 y\right)(x-2) \) (d) \( f(x, y)=\frac{x^{2 answers -
Find the Jacobian of the transformation. \[ x=2 e^{4 s+t}, y=e^{4 s-t} \] \[ \frac{\partial(x, y)}{\partial(s, t)}= \] SCALCCC4 Find the Jacobian of the transformation. \[ x=u^{3} / v^{3}, y=v^{3} / w2 answers -
2 answers
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Differentiate the function. \[ y=\frac{9 x^{2}-2}{7 x^{3}+3} \] Which of the following shows how to find the derivative of \( f(x) \) ? \( y^{\prime}=\frac{\left(9 x^{2}-2\right)\left(\frac{d}{d x}\le2 answers -
2 answers
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2 answers
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need done as soon as possible
Given \( f(x, y)=3 x^{3}+4 x^{2} y^{6}-1 y^{5} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \( f_{x x}(x, y)= \) \[ f_{x y}(x, y)= \] \[ f_{y y}(x, y)= \] \[ f_{y x}(x, y)= \]2 answers -
need done as soon as possible
Given \( f(x, y, z)=\sqrt{-4 x+3 y+2 z} \), \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
Evaluate the triple integral. \[ \iiint_{E} y d V \text {, where } E=\{(x, y, z) \mid 0 \leq x \leq 5,0 \leq y \leq x, x-y \leq z \leq x+y\} \]2 answers -
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ \begin{array}{c} y=\sqrt{x} \ln (x) \\ y^{\prime}=\left(\frac{1}{x}\right)\left(x^{\left(\frac{1}{2}\right)}+\ln (x)\left(\frac{1}{2} x^{-\left(\f2 answers -
Evaluate \( \iiint_{\mathcal{W}} f(x, y, z) d V \) for the function \( f \) and region \( \mathcal{W} \) specified: \[ f(x, y, z)=42(x+y) \quad \mathcal{W}: y \leq z \leq x, 0 \leq y \leq x, 0 \leq x2 answers -
Find all the second partial derivatives. \[ f(x, y)=x^{8} y^{6}+6 x^{6} y \] \[ f_{X x}(x, y)= \] \[ f_{x y}(x, y)= \]2 answers -
Find the first partial derivatives of the function. \[ f(x, y, z)=4 x \sin (y-z) \] \( f_{x}(x, y, z)= \) \( f_{y}(x, y, z)= \) \( f_{z}(x, y, z)= \)2 answers -
1. Find the derivatives of the following functions. (a) \( f(x)=e^{7 x^{3}+2 x} \) (b) \( y=\left(3^{x}\right)^{2} \) (f) \( f(x)=\sqrt{\frac{7 e^{5 x}}{x^{2}-5}} \) (c) \( y=3^{x^{2}} \) (g) \( y=\fr2 answers -
Find \( f_{x} \) and \( f_{y^{\prime}} \) \[ f(x, y)=\arctan \left(\frac{x}{y}\right) \] \( f_{x}(x, y)= \) \[ f_{y}(x, y)= \]2 answers -
Find the first partial derivatives of the function. \[ \begin{array}{c} f(x, y, z)=\frac{5 x}{y+z} \\ f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]2 answers -
Find the first partial derivatives of the function. \[ \begin{array}{l} f(x, y, z, t)=x y^{2} z^{7} t^{4} \\ f_{x}(x, y, z, t)= \\ f_{y}(x, y, z, t)= \\ f_{z}(x, y, z, t)= \\ f_{t}(x, y, z, t)= \end{a2 answers -
Find all the second partial derivatives. \[ f(x, y)=x^{6} y-3 x^{3} y^{2} \] \[ f_{x x}(x, y)= \] \( f_{x y}(x, y)= \) \( f_{y x}(x, y)= \) \( f_{y y}(x, y)= \)2 answers -
he indefinite integral. \( \int \cos ^{3} 6 x \sin ^{2} 6 x d x \) \[ \frac{\sin 6 x}{90}\left(4-5 \sin ^{2} 6 x+3 \sin ^{4} 6 x\right)+C \] \[ \frac{\sin 6 x}{30}\left(4-5 \sin ^{2} 6 x+3 \sin ^{4} 62 answers -
( 1 point) Find \( y \) as a function of \( x \) if \[ \begin{array}{l} y^{\prime \prime \prime}-13 y^{\prime \prime}+42 y^{\prime}=150 e^{x} \\ y(0)=13, \quad y^{\prime}(0)=25, \quad y^{\prime \prime2 answers -
Find all the second partial derivatives. \[ \begin{array}{c} f(x, y)=x^{7} y^{5}+8 x^{8} y \\ f_{x x}(x, y)=42 x^{5} y^{5}+448 x^{6} y \\ f_{x y}(x, y)=35 x^{6} y^{4}+64 x^{7} \\ f_{y x}(x, y)= \\ f_{2 answers -
(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}+36 y^{\prime}=0, \] \[ \begin{array}{l} y(0)=1, \quad y^{\prime}(0)=42, \quad y^{\prime \prime}(0)=72 \\ y(x)= \end{array2 answers -
(1 point) Find the gradient of the function \( f(x, y, z)=5 x e^{\frac{y}{2}} \sin (z) \). \[ \vec{\nabla} f(x, y, z)= \]2 answers -
only 4, thank you!
3-16 = Find \( d y / d x \) by implicit differentiation. 3. \( x^{3}+y^{3}=1 \) 4. \( 2 x^{3}+x^{2} y-x y^{3}=2 \) 5. \( x^{2}+x y-y^{2}=4 \) 6. \( y^{5}+x^{2} y^{3}=1+x^{4} y \) 7. \( y \cos x=x^{2}+2 answers -
6 please and thank you!
3-16 = Find \( d y / d x \) by implicit differentiation. 3. \( x^{3}+y^{3}=1 \) 4. \( 2 x^{3}+x^{2} y-x y^{3}=2 \) 5. \( x^{2}+x y-y^{2}=4 \) 6. \( y^{5}+x^{2} y^{3}=1+x^{4} y \) 7. \( y \cos x=x^{2}+2 answers -
8 only, thank you!
3-16 = Find \( d y / d x \) by implicit differentiation. 3. \( x^{3}+y^{3}=1 \) 4. \( 2 x^{3}+x^{2} y-x y^{3}=2 \) 5. \( x^{2}+x y-y^{2}=4 \) 6. \( y^{5}+x^{2} y^{3}=1+x^{4} y \) 7. \( y \cos x=x^{2}+2 answers -
only 10, thank you!!!
3-16 = Find \( d y / d x \) by implicit differentiation. 3. \( x^{3}+y^{3}=1 \) 4. \( 2 x^{3}+x^{2} y-x y^{3}=2 \) 5. \( x^{2}+x y-y^{2}=4 \) 6. \( y^{5}+x^{2} y^{3}=1+x^{4} y \) 7. \( y \cos x=x^{2}+2 answers