Calculus Archive: Questions from June 21, 2023
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\[ y=-5 \arccos \left(\sin ^{-1} t\right) \] \[ y=(\sin x)^{3 x} \] \( (x) \) \[ \begin{array}{l} f(x)=\operatorname{Arcsin}(\ln (3 x)) \\ y=\log _{2}\left(x^{3} \sin ^{2} x\right) \end{array} \]2 answers -
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Given: \( f(x)=(x+3)^{5}(x-2)^{4} \). Determine: a) \( f^{\prime}(x)=0 \) (exact values) b) \( f^{\prime \prime}(1) \) (exact values)2 answers -
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III. Halle la x² X hipérbola 6 ecuación 2 y 8 = 1 de la línea tangente a la en el punto (3. — 2)
III. Halle la ecuación de la linea tangente a la hipérbola \( \frac{x^{2}}{6}-\frac{y^{2}}{8}=1 \) en el punto \( (3,-2) \).2 answers -
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evaluar las integrales
Problema 5 Evaluar las siguientes integrales a. \( \int(u+4)(2 u+1) d u \) b. \( \int\left(\frac{1+\sqrt{x}+x}{\sqrt{x}}\right) d x \) c. \( \int\left(\frac{1-\sin ^{3} t}{\sin ^{2} t}\right) d t \) d2 answers -
Evaluate the integral. \[ \int \frac{\sqrt{y^{2}-81}}{y} d y, y>9 \] \[ \int \frac{\sqrt{y^{2}-81}}{y} d y= \]2 answers -
evaluar los siguientes limites usando L' Hôpital
Problema 4 Evaluar los siguientes límites a. \( \lim _{x \rightarrow 1}\left(\frac{x^{3}-2 x^{2}+1}{x^{3}-1}\right) \) b. \( \lim _{\theta \rightarrow \frac{\pi}{2}}\left(\frac{1-\sin \theta}{1+\cos0 answers -
Problema 2 Encuentre la ecuación de la recta tangente a la curva \[ y=\frac{1}{(3 x-1)^{6}} \] en \( x=0 \). Problema 3 Encuentre la ecuación de la recta tangente a la curva \[ 2\left(x^{2}+y^{2}\ri2 answers -
Problema 1 Encontrar \( \frac{d y}{d x} \) para las siguientes expresiones implícitas o explicitas. a. \( h(v)=v \sqrt[3]{1+v^{2}} \) b. \( y=(t+1)^{\frac{2}{3}}\left(2 t^{2}-1\right)^{3} \) c. \( y=2 answers -
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