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Home Question Bank Math Calculus Archive 2025 January 19

Calculus Questions from Jan 19,2025

Browse the Calculus Q&A Archive for Jan 19,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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The point \( P(3,-3) \) lies on the curve \( y=\frac{3}{2-x} \). (a) If \( Q \) is the point \( \left(x, \frac{3}{2-x}\right) \), find the slope of the secant line \( P Q \) (correct to six decimal places) for the following values of \( x \). (I) 2.9 \[ m_{P Q}= \] \( \qquad \) (ii) 2.99 \[ m_{P Q}=1 \quad x \] (iii) 2.999 \[ m_{P Q}= \] \( \qquad \) (iv) 2.9999 \[ m_{P Q}= \] \( \qquad \) (v) 3.1 \[ m_{P Q}= \] \( \qquad \) (vi) 3.01 \[ m_{P O}= \] \( \qquad \) (vii) 3.001 \[ m_{P Q}= \] \( \qquad \) (viii) 3.0001 \[ m_{P Q}= \] \( \qquad \) (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at \( P(3,-3) \). \[ m= \] \( \qquad \) (c) Using the slope from part (b), find an equation of the tangent line to the curve at \( P(3,-3) \). \( \square \) Hallar la derivada \( y=\frac{(x+1)^{3} \sqrt[4]{(x-2)^{3}}}{\sqrt[5]{(x-3)^{2}}} \) 3. Исследовать на экстремум функцию \( f(x, y)=-x^{2}+x y-y^{2}-9 x+3 y-20 \) Hallar la derivada de las funciones \( y=\frac{\operatorname{arcsen}\left(\ln x^{3}\right) \operatorname{sen}^{3}(x)}{\operatorname{sen} x} \) La posición de un cuerpo está descrita por \( s(t) = -4t^2 + 32t + 10 \). Calcula la aceleración del cuerpo en función del tiempo. 2. Найти уравнение касательной и нормали к поверхности \( x^{2}+x y+2 y^{2}+5 z^{2}=24 \) в точке \( (1,1,2) \). Hallar la derivada de las funciones \( y=\frac{\operatorname{arcsen}\left(\ln x^{3}\right) \operatorname{sen}^{3}(x)}{\operatorname{sen} x} \) Exercice 2 Soit \( X_{t}=\int_{0}^{t} s d B_{s} \) Д. Calculer \( E\left(X_{t}\right) \) et \( \operatorname{Var}\left(X_{t}\right) \) 2. Quelle est la loi de \( X_{t} \) 3. Calculer \( d\left(t B_{t}\right) \) à l'aide de la formule d'Itô. 4. En déduire une relation entre \( X_{t} \) et \( Y_{t}=\int_{0}^{t} B_{s} d s \) 5. Calculer \( \operatorname{Var}\left(Y_{t}\right) \) 0. Quelle est la loi de \( Y_{t} \) Utiliza la linealización para aproximar los oiguientes valores de las funciones a. \( f(x)=\sqrt{100} \); como sugerencia, puedes conviderar \( x_{0}=2.5^{1}=97.65 \). b. \( \log _{3}(1.25) \) a) \( F(x)=8 x^{4}-2 x^{-5}+5 x^{\frac{2}{4}}+8 \)
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