Calculus Archive: Questions from September 04, 2023
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Elimination of Arbitrary Constant
1.) \( y=c x^{2} \) 2.) \( y=c x+c \) 3. ) \( y=c_{1} e^{2 x}+c_{2} e^{3 x} \) 4.) \( y=a x^{2}+b x+c \) 5. ) \( y=c_{1} \cos x+c_{2} \sin \) 6. ) \( y=c_{1} e^{-x}+c_{2} e^{2 x} \)1 answer -
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Number 49 please, ill drop a like!
Find \( d y / d x \) in Exercises \( 45-56 \). 45. \( y=\int_{0}^{x} \sqrt{1+t^{2}} d t \) 46. \( y=\int_{1}^{x} \frac{1}{t} d t, \quad x> \) 47. \( y=\int_{\sqrt{x}}^{0} \sin t^{2} d t \) 48. \( y=x1 answer -
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Please be neat and clear.
1. Find the derivative of the following functions. a) \( y=e^{-5 x} \) b) \( y=e^{5-7 x} \) c) \( y=x e^{x}-e^{x} \) d) \( y=\ln \left(3 x e^{-x}\right) \) e) \( y=\ln \left(2 e^{-t} \sin t\right) \)1 answer -
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26. y cos x, y = 2 cos x, 0≤x≤ 2π - 27. y = cos x, y sin 2x, 0≤x≤ TT/2 sketch and find area by integration
26. \( y=\cos x, \quad y=2-\cos x, \quad 0 \leqslant x \leqslant 2 \pi \) 27. \( y=\cos x, \quad y=\sin 2 x, \quad 0 \leqslant x \leqslant \pi / 2 \)1 answer -
I. Considere la función \( w=\operatorname{sen}(2 x+3 y) \quad \) donde \( x=s+t \quad \) y \( y=s-t \) para determinar a) \( \frac{\partial w}{\partial s} \quad \) para \( s=0 \quad y \quad t=\frac{1 answer -
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questions D through I. please be neat and clear.
1. Find the derivative of the following functions. a) \( y=e^{-5 x} \) b) \( y=e^{5-7 x} \) c) \( y=x e^{x}-e^{x} \) d) \( y=\ln \left(3 x e^{-x}\right) \) e) \( y=\ln \left(2 e^{-t} \sin t\right) \)1 answer -
1. Sean \( f(x, y)=\sin \left(x-y+y^{3}\right) \) y \( A \) el punto con coordenadas \( x=0, y=1 \). a) (2 puntos) Calcular la tasa de cambio de la función \( f(x, y) \) en el punto \( A \) en la dir1 answer -
If \( f(x)=\left\{\begin{array}{ll}-2 x^{8} \sin \frac{1}{x} & \text { if } x \neq 0 \\ 0 & \text { if } x=0\end{array}\right. \) determine whether or not \( f^{\prime}(0) \) exists. \( \lim _{h \r1 answer -
Evaluate the integral \[ \int_{0}^{1} \int_{0}^{x} \int_{0}^{1+x+y} f(x, y, z) d z d y d x \] where \( f(x, y, z)=1 \).1 answer -
For Problems 1-14, solve the given differential equation. 1. \( y^{\prime \prime}-2 y^{\prime}=6 e^{3 x} \). 2. \( y^{\prime \prime}=2 x^{-1} y^{\prime}+4 x^{2} \). 3. \( (x-1)(x-2) y^{\prime \prime}=1 answer -
#26 please
\( \left(4 y-y^{2}+4 y^{3}+1\right)^{-2 / 3}\left(12 y^{2}-2 y+4\right) d y \quad y=3(\sin x) \sqrt{1} \) \( \left(y^{3}+6 y^{2}-12 y+9\right)^{-1 / 2}\left(y^{2}+4 y-4\right) d y \) \( \begin{array}{1 answer -
5. Find the area of the region. (a) \( y=\sin x, y=x, x=\pi / 2, x=\pi \) (b) \( x=1-y^{2}, x=y^{2}-1 \) (c) \( 4 x+y^{2}=12, x=y \) (d) \( y=x^{2}, y=4 x-x^{2} \) (e) \( x=2 y^{2}, x=4+y^{2} \) (f) \1 answer -
1. Para el campo vectorial \( \overrightarrow{\mathbf{F}}=-y \hat{\mathbf{i}}+x \hat{\mathbf{j}} \), evalúa la integral de lÃnea \( \int_{C} \overrightarrow{\mathbf{F}} \cdot d \overrightarrow{\math1 answer -
Demuestre la convergencia o divergencia de las series. Si es convergente encuentre su suma. 1. \( \sum_{n=1}^{\infty}\left(1+\frac{2}{n}\right)^{n} \) 2. \( \sum_{n=0}^{\infty}\left(\frac{2}{3}\right)1 answer -
help asap please
Find \( y \) by implicit differentiation. Match the equations defining \( y \) implicitly with the letters labe 1. \( 4 \sin (x-y)=2 y \cos x \) 2. \( 4 \cos (x-y)=2 y \cos x \) 3. \( 4 \cos (x-y)=2 y1 answer -
biol
La anterior es la gráfica de \( f(x) \), junto a los valores que corresponden al "signed área" de las distintas regiones sombreadas. \[ \int_{-6}^{3} f(x) d x= \] Respuesta a. 7 b. -5 c. 2 d. -31 answer -
Questions H and I only. Please be neat and clear.
1. Find the derivative of the following functions. a) \( y=e^{-5 x} \) b) \( y=e^{5-7 x} \) c) \( y=x e^{x}-e^{x} \) d) \( y=\ln \left(3 x e^{-x}\right) \) e) \( y=\ln \left(2 e^{-t} \sin t\right) \)1 answer -
/1 PUNTOS] ZILLDIFFEQLA9 2.4.024. Resuelva el problema con valores iniciales. \[ \left(\frac{3 y^{2}-t^{2}}{y^{5}}\right) \frac{d y}{d t}+\frac{t}{2 y^{4}}=0, \quad y(1)=1 \] \[ \frac{-3}{2 y^{2}}+\fr1 answer -
Determine si la ecuación diferencial dada es exacta. Si es exacta, resuélvala. (Si es no exacta, indique NO. Para la función de "sen()", utilice "sin()". Por ejemplo, "sen(x)" se escribe como \( "1 answer -
If \( \frac{d}{d x}\left(f\left(3 x^{4}\right)\right)=5 x^{4} \), calculate \( f^{\prime}(x) \). \[ f^{\prime}(x)= \]1 answer -
Questions 1,3,5,9,19,25,31
Exercise Set 2.5 Find \( \frac{d y}{d x} \). 1. \( y=x^{7} \) 3. \( y=3 x^{2}+3 \) 2. \( y=x^{8} \) 5. \( y=x^{3}(4) \) 4. \( y=5 x^{4}-8 \) 7. \( y=3 x^{2 / 3}+1 \) 6. \( y=(\sin x)(10) \) 9. \( y=\s1 answer