Calculus Archive: Questions from March 01, 2023
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\[ \begin{array}{l} \text { If } y=A x \cos (\ln x)+B x \sin (\ln x) \text {, then } y^{\prime}= \\ \text {, } y^{\prime \prime}= \\ \end{array} \] , Hence, \[ x^{2} y^{\prime \prime}-x y^{\prime}+2 y2 answers -
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Diffcrentiate. 1. \( f(x)=3 x^{2}-7 x+1 \) 3. \( h(x)=\ln (10 x) \) 5. \( f(x)=\frac{1}{\sqrt{x}}-\frac{2}{x} \) 2. \( y=2 x^{3}-e^{7 x}+\pi \) 4. \( g(x)=\frac{3 x^{2}-6 x^{3}}{x^{2}} \) 6. \( P(x)=\2 answers -
10. Solve for \( x \) and \( y \). \[ \left[\begin{array}{ccc} 4 & 1 & 3 \\ -2 & x & 1 \end{array}\right]\left[\begin{array}{cc} 9 & -2 \\ 2 & 1 \\ -1 & 1 \end{array}\right]=\left[\begin{array}{cc} y2 answers -
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En el proceso de resolver la integral \( \int \frac{x-4}{(x-7)(x-5)} d x \) debemos usar fracciones parciales Supongamos que reescribimos la integral como \[ \int \frac{x-4}{(x-7)(x-5)} d x=\int \frac2 answers -
La concentración de una droga en el cuerpo, medido en \( \mu g / m L \), esta dada por \[ C(t)=17,58 t e^{-t} \] donde \( t \) se mide en horas. 1) La disponibilidad de la droga en el cuerpo durante2 answers -
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Find \( y^{\prime} \) and \( y^{\prime} \). \[ \begin{array}{r} y=\sqrt{\sin (x)} \\ y^{\prime}=\sqrt{\frac{\cos (x)}{2 \sqrt{\sin (x)}}} \end{array} \]2 answers -
31. Find \( \frac{d^{4} y}{d x^{4}} \) if \( y+x^{3}=\cos x-\sin x \) 32. Find \( \frac{d^{34} y}{d x^{34}} \) if \( y=\cos x \) 33. Find \( \frac{d^{2} y}{d x^{2}} \) if \( y=\cot x \) 34. Find \( \f2 answers -
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Determine \( \int y d x \) if : 2.1 \( y=e^{\sin (2 x)} \cos (2 x) \) 2.2 \( y=e^{x} \cdot 2^{x} \) 2.3. \( y=\cos ^{5}(2 x) \) \( 2.4 \quad y=\sqrt{5-9 x-3 x^{2}} \) 2.5 \( y=\sin ^{2}(2 x)-\cos ^{2}2 answers -
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2) Find the derivative of a) \( y=\left(x-2 x^{4}\right)^{5}(\sin 2 x) \). b) \( y=\frac{e^{\tan x}}{\sqrt{3 x^{6}-\sec \frac{1}{x}}} \) c) \( y=\frac{6 e^{x}}{\sqrt{8 x+\ln x}} \) d) \( f(x)=\cos \le2 answers -
if \( y=\frac{\cos x}{x} \), then \( y^{\prime}= \) and \( y^{\prime \prime}= \) Hence, \( x y^{\prime \prime}+2 y^{\prime}=1 \)2 answers -
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evaluate the intergal #22 & #25
1. \( \int \tan x \sec ^{3} x d x \) 22. \( \int \tan ^{2} \theta \sec ^{4} \theta d \theta \) 3. \( \int \tan ^{2} x d x \) 24. \( \int\left(\tan ^{2} x+\tan ^{4} x\right) d x \) 5. \( \int \tan ^{4}2 answers -
Evaluate the double integral. \[ \iint_{D} 4 x \sqrt{y^{2}-x^{2}} d A, D=\{(x, y) \mid 0 \leq y \leq 4,0 \leq x \leq y\} \]2 answers -
Let \( f(x, y)=7 x^{3} y-7 x y^{4} \). Calculate \[ \begin{array}{ll} f(1,0)= & f(0,0)= \\ f_{x}(1, y)= & f_{x}(x, 1)= \\ f_{y}(1,0)= & f_{x x}(x, y)= \\ f_{x x y y}(x, y)= & f_{x x x}(x, y)= \end{arr2 answers -
c033exp13
If \( y=\frac{3 \cos x-9 \sin x}{8 \sin x} \), then If \( y=\frac{3 \cos x-9 \sin x}{8 \sin x} \), then \[ f^{\prime}(x)= \]2 answers -
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number 16 find the exact length of the curve
9-24 Find the exact length of the curve. 9. \( y=\frac{2}{3} x^{3 / 2}, \quad 0 \leqslant x \leqslant 2 \) 10. \( y=(x+4)^{3 / 2}, \quad 0 \leqslant x \leqslant 4 \) 11. \( y=\frac{2}{3}\left(1+x^{2}\2 answers -
Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-15 y^{\prime \prime}+56 y^{\prime}=0 \] \[ y(0)=5, y^{\prime}(0)=7, y^{\prime \prime}(0)=8 \text {. } \] \( y(x)= \)2 answers -
SCALCET9 3.4.053. O/2 Submissions Used Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=\cos (\sin (5 \theta)) \] \[ y^{\prime}= \] \[ y^{\prime \prime}= \]2 answers -
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Let \( f(x, y)=3 x^{3} y-2 x y^{4} \). Calculate \[ \begin{array}{ll} f(1,0)= & f(0,0)= \\ f_{x}(1, y)= & f_{x}(x, 1)= \\ f_{y}(1,0)= & f_{x x}(x, y)= \\ f_{x x y y}(x, y)= & f_{x x x}(x, y)= \end{arr2 answers -
i need help on 18
13-20 n Sketch the graph of the function. 13. \( f(x, y)=10-4 x-5 y \) 14. \( f(x, y)=2-x \) 15. \( f(x, y)=y^{2}+1 \) 16. \( f(x, y)=e^{-y} \) 17. \( f(x, y)=9-x^{2}-9 y^{2} \) 18. \( f(x, y)^{-}=1+22 answers -
#27, 37, and 39
26. \( \left(1+x^{2}\right) y^{2}=x^{3} y \) 27. \( y^{\prime}=x \sec y \) 28. \( \frac{d y}{d \theta}=\tan y \) 29. \( \frac{d y}{d t}=y \tan t \) 30. \( \frac{d x}{d t}=t \tan x \) In Exercises \( 32 answers -
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6- differentiate \[ y=e^{\tan \theta} \] 7- Differentiate \[ s(t)=\sqrt{\frac{1+\sin t}{1+\cos t}} \]2 answers -
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(1 point) Let \( f(x, y, z)=\frac{x^{2}-3 y^{2}}{y^{2}+3 z^{2}} \). Then \[ \begin{array}{l} f_{x}(x, y, z) \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]2 answers -
Use the Chain Rule to find \( d w / d t \). \[ \begin{array}{c} w=\ln \left(\sqrt{x^{2}+y^{2}+z^{2}}\right), \quad x=8 \sin (t), \quad y=6 \cos (t), \\ \frac{d w}{d t}=\frac{64 \sin (2 t)-36 \sin (2 t2 answers -
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Find \( y^{\prime} \) for the function. \[ \begin{array}{l} \sqrt[4]{(y+3)^{3}}=-1+x \\ y^{\prime}= \end{array} \]2 answers -
Compute the gradient vector fields of the following functions: A. \( f(x, y)=5 x^{2}+9 y^{2} \) \( \nabla f(x, y)=\quad \mathbf{i}+\quad \mathbf{j} \) B. \( f(x, y)=x^{6} y^{10} \) \( \nabla f(x, y)=\2 answers -
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4. Demuestre que \[ \int_{0}^{2 \pi} \frac{d \theta}{a \pm b \cos \theta}=\int_{0}^{2 \pi} \frac{d \theta}{a \pm b \operatorname{sen} \theta}=\frac{2 \pi}{\sqrt{a^{2}-b^{2}}} \] para \( |a|>|b| \). ¿2 answers -
calculate the following limits
b. \[ \begin{array}{l} \lim _{x \rightarrow \infty} \frac{x^{2}+4 x^{2} \ln x+x^{2} e^{x}}{x^{3}+x \ln x+3 x e^{x}} \\ \lim _{x \rightarrow \infty} \frac{\sqrt[6]{x^{17}+x^{2}}}{\sqrt[7]{x^{12}+x^{3}}2 answers -
Find \( d y / d x \) \[ \begin{array}{c} y=[\cos x]^{e^{3 x}} \\ y=\frac{e^{5 x}\left(x^{2}+9\right)^{4}}{\sqrt[3]{x} \tan ^{3} x} \\ y^{2}=2 x y-\cot y \end{array} \]2 answers -
Help Entering Answers (1 point) Find the gradient vector field of the following functions: \[ f(x, y)=6 x e^{2 x y}, \quad \nabla f(x, y)= \] \[ g(x, y)=2 \tan (2 x-y), \quad \nabla g(x, y)= \] \[ h(x2 answers -
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Find an exponential growth model \( y=y_{0} e^{k t} \) that satisfies the stated conditions. \[ y(1)=1 ; y(28)=134 \] \[ \begin{array}{l} y=0.83 e^{0.181 t} \\ y=0.59 e^{-0.26 t} \\ y=0.59 e^{0.26 t}2 answers -
57. \( f(x, y)=3 x^{2} y-6 x y^{4}, \frac{\partial^{2} f}{\partial x^{2}} \) and \( \frac{\partial^{2} f}{\partial y^{2}} \)2 answers -
If \( y^{\prime \prime}=\frac{1}{(x+1)^{2}}, y(0)=2 \cdot y^{\prime}(0)=1^{\text {then }} y^{\prime}= \)2 answers -
Find a possible formula for the graph below. \[ \begin{array}{ll} y=k(x+5)(x+1)(x-3), & k>0 \\ y=k(x+5)^{2}(x+1)^{2}(x-3), & k2 answers