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Calculus Archive: Questions from October 01, 2022

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  If \( f(x)=\tan 5 x \) Find \( f^{\prime}(4) \)
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  \[ \psi(y)=\left\{\begin{array}{ll} D \psi_{I}(y)=D\left(\cos (2 \epsilon)+\frac{\sqrt{\gamma^{2}-\epsilon^{2}}}{\epsilon} \sin (2 \epsilon)\right) e^{\sqrt{\gamma^{2}-\epsilon^{2}} y} & -\infty
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  Evaluate the integral of the function \( f(x, y)=y \mathrm{e}^{y x} \) over the region \[ R=\{(x, y):-2 \leq x \leq 1,0 \leq y \leq 2\} \] \[ \iint_{R} f(x, y) d A= \]
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  Q2. Evaluate the integral \( \int \sin ^{2}(7 x) \cos ^{3}(7 x) d x \)
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  (3) Find differential \[ f(x, y)=x \sin (x y) \]
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  (1 point) If \( f(x)=4 x^{2}-10 x-36 \) \( f^{\prime}(x)= \) (1 point) If \( f(x)=6 e^{x}+2 \) \[ f^{\prime}(x)= \] (1 point) Find \( y^{\prime} \) for \( y=\frac{1}{x^{11}} \). \[ y^{\prime}= \]
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  2.) (2pts) Solve the DE \( \frac{d y}{d x}=\frac{(\sin x+\sin 2 x) y^{3}}{\cos ^{2} x+1} \).
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  3.) (2pts) Solve the IVP \( \quad(x+1)^{2} \frac{d y}{d x}+y=\frac{1}{x+1}, \quad y(0)=0 \).
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  (1 point) Given \( f(x, y)=-\left(6 x^{6} y+8 x y^{6}\right) \). Compute: \[ \begin{array}{l} \frac{\partial^{2} f}{\partial x^{2}}= \\ \frac{\partial^{2} f}{\partial y^{2}}= \end{array} \]
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  Dada la función \( f(x)=\frac{3 x+2}{6 x-1} \), encontrar \( f^{\prime}(3) \), usando la regla del cociente. En el numerador de la derivada tenemos: \[ u v^{\prime}-v u^{\prime}=1 \quad 1 \quad 3-(\q
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  Take the derivative. (a) \( y=(\sqrt{x}+1)^{100} \) \( J(\theta)=\tan ^{2}(3 \theta) \) \( f(x)=\sin (\cos (\sqrt{x+1})) \) \( y=\sqrt{x+\sqrt{x+\sqrt{x}}} \)
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• i want all answers please );
  (a) \( y=\left(x^{2}+5\right)^{10} \) (b) \( y=\sqrt{1+6 x} \) 4. Find \( d y / d x \). (a) \( y=\sin (3 x+2) \) (b) \( y=\left(x^{2} \tan x\right)^{4} \) 5. Suppose that \( f(2)=3, f^{\prime}(2)=4, g
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• 1. Consider ________ to determine _________. 2. Consider _______ to determine _________. 3. Determine the directional derivative of the function in the direction of PQ f (x, y) = x2 + 3y2 where P(1,1)
  I. Considere \( w=x^{2}-2 x y+y^{2}, x=r+\theta, y=r-\theta \) para determinar \( \frac{\partial w}{\partial r} \& \frac{\partial w}{\partial \theta} \). II. Considere \( w=x y \cos (z), x=t, y=t^{2}
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  Find the general solution of \( y^{\prime \prime}-2 y^{\prime}+y=6 x e^{x} \) \( y=\left(C_{1}+C_{2} x^{2}\right) e^{x} \) None of these \( y=\left(C_{1}+C_{2} x+x^{3}\right) e^{x} \) \( y=\left(C_{1}
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  Find the general solution of \[ y^{\prime \prime}+4 y^{\prime}+4 y=x e^{2 x} \] \[ y=\left(C_{1}+C_{2} x\right) e^{-2 x}+\left(\frac{x}{16}-\frac{1}{32}\right) e^{2 x} \] \[ y=\left(C_{1}+C_{2} x\righ
  2 answers
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  Find the general solution of \( y^{\prime \prime}-2 y^{\prime}+y=6 x e^{x} \) \( y=\left(C_{1}+C_{2} x^{2}\right) e^{x} \) None of these \[ \begin{array}{l} y=\left(C_{1}+C_{2} x+x^{3}\right) e^{x} \\
  2 answers

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  \( (\sin y-y \sin x) d x+(\cos x+x \cos y-y) d y=0 \)
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  Differentiate the function. \[ y=\frac{x^{7}-7 x^{2}+7}{x} \]
  1 answer

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  \( \left(y^{2}+3 x y^{3}\right) d x+(1-x y) d y=0 \).
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  Solve the IVP: 4. \( y^{\prime \prime}-y=0 ; y(0)=y^{\prime}(0)=1 \).
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• Given function f(x, y) = e^(x−y) + sin(x + y) Let x = r / s , y = −rs, Find fs at (r, s) = (1, 1).
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• only question #6 please.
  5. \( \quad y^{\prime}-x y=x^{3} y^{3} ; \quad\{-3 \leq x \leq 3,2 \leq y \geq 2\} \) 6. \( y^{\prime}-\frac{1+x}{3 x} y=y^{4} ; \quad\{-2 \leq x \leq 2,-2 \leq y \leq 2\} \)
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  Evaluate \[ \int_{0}^{\pi} e^{\cos \theta} \sin 2 \theta d \theta \] (Hint: Use the identity \( \sin 2 \theta=2 \sin \theta \cos \theta \).)
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  Find the partial derivatives of the function \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \end{array} \] \[ f(x, y)=x y e^{1 y} \]
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• Find and simplify the function values. f(x, y) = 9x + y2 (a) f(x + Δx, y) − f(x, y) Δx (b) f(x, y + Δy) − f(x, y) Δy
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  2. Solve the initial value problem \[ y^{\prime}+\frac{2}{t} y=t^{2}+\frac{1}{t^{3}} \quad y(1)=3 \]
  2 answers