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Calculus Archive: Questions from March 05, 2023

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  Solve the initial-value problem: (a) \( (5 \) marks \( ) y^{\prime}=\frac{x y \sin x}{y+1}, y(0)=1 \). (b) \( \left(5\right. \) marks) \( 2 x y^{\prime}+y=6 x, x>0, y(4)=20 \).
  3 answers
• Primer pa√≠s en esta nueva forma de gobierno
  2 answers
• Felix X. Balmis que aportaciones tuvo
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• Que aportaci√≥n tuvo Van Behring y Kitasato
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• La diferencia entre c y 3 es mayor o igual que 21.
  0 answers
• Evaluate the expression. Simplify if possible. 8(6)/(8)+(-6(2)/(4))
  2 answers
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  The solution of the following differential equation \( y^{\prime}=\left(y^{2}+1\right)\left(\cos ^{2}(x)-\frac{1}{2}\right) \) is: Select one: a. \( \left(1+y^{2}\right)^{-1}=\frac{\sin (2 x)}{4}+c \)
  2 answers
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  11. \( \int \frac{\sqrt{y^{2}-49}}{y} d y, \quad y>7 \) 13. \( \int \frac{d x}{x^{2} \sqrt{x^{2}-1}}, x>1 \)
  2 answers

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  Determine \( y^{\prime} \) when \[ y=x^{-x} \text {. } \] 1. \( y^{\prime}=x y(2 \ln x-1) \) 2. \( y^{\prime}=\frac{y}{x^{2}}(\ln x-1) \) 3. \( y^{\prime}=x y(2 \ln x+1) \) 4. \( y^{\prime}=-x y(2 \ln
  2 answers

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  Suppose \( y=e^{3 x^{2}+3 x} \) \[ \frac{d y}{d x}= \]
  2 answers
• Differentiate the following functions?
  \( y=x^{3} \sec x+\sqrt{x} \sin x \) \( y=\frac{x}{2-\tan x} \) \( [2 \mathrm{pts}] y=\tan x \sec x \) [3 pts] \( y=x^{3} \sec x+\sqrt{x} \sin x \) \( [2 \mathrm{pts}] y=\frac{x}{2-\tan x} \)
  2 answers

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  (2) Solve the IVP: \( \cos ^{2}(y) d x-x d y=0, y(1)=\frac{\pi}{4} \). (3) Solve: \( x y^{\prime}=y-x \tan \left(\frac{y}{x}\right) \).
  2 answers
• quotient rule
  \( y=\frac{7+\sin x}{x+\cos x} \) Differentiate \( y=\frac{\sin x}{x^{5}} \). \[ y^{\prime}= \]
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  Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ \begin{array}{l} y=e^{\alpha x} \sin \beta x \\ y^{\prime}= \\ y^{\prime \prime}= \end{array} \]
  2 answers
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  . (3 marks) Let \( \int_{0}^{1} \int_{0}^{2-2 x} \int_{0}^{2-2 x-y} f(x, y, z) d z d y d x=\int_{a}^{b} \int_{g_{1}(z)}^{g_{2}(z)} \int_{h_{1}(y, z)}^{h_{2}(y, z)} f(x, y, z) d x d y d z \) Find \[ a=
  2 answers

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  Differentiate the function. \[ y=\frac{5 x^{2}-2}{4 x^{3}+5} \]
  2 answers
• Let f(x, y) = (3y(x^3)+y^2)/(2(x^6)+y^2) . Find lim (x,y)→(0,0) of f(x, y)
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  (1 point) Differentiate \( y=2^{\sin \pi x} \). \[ y^{\prime}= \]
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  Reverse the order of integration in the inte\( \mathrm{gral} \) \[ I=\int_{0}^{2} \int_{x / 2}^{1} f(x, y) d y d x, \] \[ \begin{array}{c} I=\int_{0}^{2} \int_{0}^{y / 2} f(x, y) d x d y \\ 2 I=\int_{
  2 answers

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  6. Solve the initial-value problem: (a) \( (5 \) marks \( ) y^{\prime}=\frac{x y \sin x}{y+1}, y(0)=1 \). (b) (5 marks) \( 2 x y^{\prime}+y=6 x, x>0, y(4)=20 \).
  2 answers
• questions 47
  \( \begin{array}{l}y=\frac{-}{x} \\ y=\frac{8}{x^{5}}\end{array} \)
  0 answers
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  Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ \begin{array}{c} y=e^{a x} \sin (\beta x) \\ y^{\prime}=e^{a x}(\beta \cos \beta x+\operatorname{asin} \beta x) \\ y^{\prime \prime}=e^{a x\left(\
  2 answers

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  Solve \[ y^{\prime \prime}+1 y=0, \quad y\left(\frac{\pi}{2}\right)=1, \quad y^{\prime}\left(\frac{\pi}{2}\right)=3 \]
  2 answers
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  Given \( f(x, y)=6 \sqrt{5 x^{3}+2 y+4 x y^{5}} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \]
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  Given \( f(x, y)=4 x^{5}-4 x y^{4}+2 y^{6} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \]
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  Given \( f(x, y)=-2 x^{6}-4 x y^{2}+y^{3} \), \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]
  2 answers
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  Given \( f(x, y)=7 x^{8} \cos \left(y^{4}\right) \), find \[ \begin{array}{c} f_{x y}(x, y)= \\ f_{y y}(x, y)= \end{array} \]
  2 answers

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  Determine \( y^{\prime} \) when 1. \( y^{\prime}=\frac{\sin x(1-\cos x)}{2+\cos x} \) \[ e^{y+\cos x}=2+\cos x \] 2. \( y^{\prime}=\frac{\sin x(1+\cos x)}{2+\cos x} \) 3. \( y^{\prime}=\frac{\cos x(1+
  2 answers
• Ejercicios de Cálculo de áreas Encuentra el área limitada por las gráficas siguientes, estos tipos de figuras aparecen en los ciclos termodinámicos. ​​​​​​​ ​​​​​​​​
  2 answers
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  Calculate \( y^{(k)}(0) \) for \( 0 \leq k \leq 5 \), where \( y=7 x^{4}+a x^{3}+b x^{2}+c x+d \) (with a,b,c, d the constants) \[ \begin{array}{l} y^{(0)}(0)= \\ y^{(1)}(0)= \\ y^{(2)}(0)= \\ y^{(3)}
  2 answers
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  Find each limit. \[ f(x, y)=\frac{3}{x+y} \] (a) \( \lim _{\Delta x \rightarrow 0} \frac{f(x+\Delta x, y)-f(x, y)}{\Delta x} \) (b) \( \lim _{\Delta y \rightarrow 0} \frac{f(x, y+\Delta y)-f(x, y)}{\D
  2 answers
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  Solve the differential equation \( \frac{d y}{d x}-\frac{2}{x} y=\frac{1}{x^{2}} y^{2} \) given that when \( x=1, y=1 \) Select one: \[ \begin{array}{l} y=\frac{x^{2}}{-x+c} \\ y=\frac{x^{2}}{2-x} \\
  2 answers
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  \( f(x)=x^{3}-3 x^{2}+3 x-15 \) \[ f^{\prime}(0)= \] \[ f^{\prime}(2)= \] \[ f^{\prime}(-3)= \]
  2 answers
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  (1 point) Match each of the following differential equations with a solution from the list below. 1. \( y^{\prime \prime}-13 y^{\prime}+40 y=0 \) 2. \( 2 x^{2} y^{\prime \prime}+3 x y^{\prime}=y \) 3.
  2 answers
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  Evaluate the integral. \[ \int \frac{\cos y d y}{\sin ^{2} y+3 \sin y-18} \] \[ \int \frac{\cos y d y}{\sin ^{2} y+3 \sin y-18}= \] (Type an exact answer.)
  2 answers

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  Find \( \iint_{R} f(x, y) d A \) where \( f(x, y)=3 x+1 \) and \( R=[1,6] \times[4,5] \). \( \iint_{R} f(x, y) d A= \)
  2 answers
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  Find all the second order partial derivatives of \( g(x, y)=x^{5} y+2 \sin (y)+y \cos (x) \). \[ \begin{array}{l} \frac{\partial^{2} g}{\partial x^{2}}= \\ \frac{\partial^{2} g}{\partial y \partial x}
  2 answers
• Number 8
  3-8 Set up, but do not evaluate, an integral for the length of the curve. 3. \( y=x^{3}, \quad 0 \leqslant x \leqslant 2 \) 4. \( y=e^{x}, \quad 1 \leqslant x \leqslant 3 \) 5. \( y=x-\ln x, \quad 1 \
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  Complete the table.
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  5. Find \( y^{\prime} \) if \( y=\sqrt{\frac{x^{2}-5}{x^{2}+4}} \) two different ways.
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  Find \( d y / d x \) 9. \( y=\tan ^{-1}(\ln (x)) \) 10. \( y=2 \sin ^{-1}\left(x^{2}\right) \)
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• If g(x) = 0.5x + 6 if x < 0 6 − x if 0 ≤ x < 4, 0 if x > 4 find the following. (a) g(−6) (b) g(0) (c) g(9) (d) g(2.5)
  2 answers
• If g(x) = 0.5x + 6 if x < 0 6 − x if 0 ≤ x < 4, 0 if x > 4 find the following. (a) g(−6) (b) g(0) (c) g(9) (d) g(2.5)
  2 answers
• If g(x) = 0.5x + 6 if x < 0 6 − x if 0 ≤ x < 4, 0 if x > 4 find the following. (a) g(−6) (b) g(0) (c) g(9) (d) g(2.5)
  2 answers