Calculus Archive: Questions from July 21, 2022
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True or False? If \( \quad y=3 \sin \left(2 x^{4}\right) \) then \( y^{\prime}=8 x^{3} \cos \left(2 x^{4}\right) \) True False QUESTION 5 True or False? If \( y=-\sin \left(x^{4}\right) \quad \) then1 answer -
True or False? If \( y=3 \sin \left(2 x^{4}\right) \quad \) then \( \quad y^{\prime}=8 x^{3} \cos \left(2 x^{4}\right) \) True False QUESTION 5 True or False? If \( y=-\sin \left(x^{4}\right) \quad \)1 answer -
True or False? If \( \quad y=3 \csc \left(4 x^{3}\right) \quad \) then \( \quad y^{\prime}=-36 x^{2} \csc \left(4 x^{3}\right) \cot \left(4 x^{3}\right) \) True False3 answers -
True or False? If \( \quad y=3 \sin \left(2 x^{4}\right) \quad \) then \( \quad y^{\prime}=8 x^{3} \cos \left(2 x^{4}\right) \)1 answer -
True or False? If \( \quad y=-\sin \left(x^{4}\right) \quad \) then \( \quad y^{\prime}=-\cos \left(x^{4}\right) \)1 answer -
help please asap!!!
1) Find \( \frac{d y}{d x} \) for each function: a. \( y=5 x^{3}-7 x^{2} \) [1] b. \( y=2 x-5 \) [1] c. \( y=\ln \left(x^{2}+1\right) \) [2] d. \( y=x^{2} \sin x \) [2] e. \( y=\sqrt{x}-\frac{1}{\sqrt1 answer -
Compute the double integral \[ \iint_{D} \cos \left(9 x^{2}+4 y^{2}\right) d A \] where \( D=\left\{\left((x, y) \mid 9 x^{2}+4 y^{2} \leq 1\right\}\right. \).1 answer -
8,9,10
Suppose that \( f(x, y)=y \sqrt{x^{3}+1} \) for \( \{(x, y) \mid 0 \leq y \leq x \leq 2\} \) Evaluate the double integral of \( f(x, y) \) over \( D \). Suppose that \( f(x, y)=\frac{y}{1+x} \) for \1 answer -
(6) \( y=\sqrt{-2 x^{4}+5 x^{2}-6}, \quad y^{\prime}= \) (A) \( \left(-8 x^{3}+10 x\right)^{-\frac{1}{2}} \) (C) \( (-2 \) (B) \( \frac{1}{2}\left(-2 x^{3}+10 x-6\right)^{\frac{1}{2}}\left(-8 x^{3}+101 answer -
1 answer
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Find an explicit solution of the initial value problem
\[ \frac{d x}{d t}=4\left(x^{2}+1\right), \quad x\left(\frac{\pi}{4}\right)=1 . \] Seleccione la respuesta correcta: (a) \( x=\tan (\operatorname{sen}(t)) \) (b) \( x=\tan \left(4 t-\frac{3 \pi}{4}\ri1 answer -
Find the solution of the exact differential equation (e) this differential equation is not exact (f) none of the above
\[ \left(y-x^{3}\right) d x+\left(x+y^{3}\right) d y=0 \] Seleccione la respuesta correcta. (a) \( x y+\frac{x^{2}}{2}-\frac{y^{4}}{4}=C \) (b) \( x y-\frac{x^{4}}{4}+\frac{y^{4}}{4}=C \) (c) \( x y+\1 answer -
1 answer
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4) Find \( y \) '. a) \( y=(\ln (2 x))^{\cos x} \) \[ \tan (x) \sin \left(e^{y}\right)+y^{2} \sin \left(x^{3}\right)=1 \]1 answer -
4) Find \( y \) : a) \( y=(\ln (2 x))^{\cos x} \) b) \( \tan (x) \sin \left(e^{y}\right)+y^{2} \sin \left(x^{3}\right)=1 \)1 answer -
7. \( z=(x-y)^{5}, x=s^{2} t, y=s t^{2} \) 9. \( z=\ln (3 x+2 y), x=s \sin t, y=t \cos s \) 11. \( z=e^{r} \cos \theta, r=s t, \theta=\sqrt{s^{2}+t^{2}} \)3 answers -
11. \( f(x, y)=e^{x} \sin y, \quad\left(0, \frac{\pi}{3}\right), \quad \mathbf{v}=\langle-6,8\rangle \) 13. \( g(s, t)=s \sqrt{t}, \quad(2,4), \quad \mathbf{v}=2 \mathbf{i}-\mathbf{j} \) 15. \( f(x, y1 answer -
Evaluate the double integral. \( \int_{1}^{5} \int_{0}^{x}(8 x-2 y) d y d x \) \( \int_{0}^{1} \int_{0}^{y} x e^{y^{3}} d x d y \) \( \int_{0}^{1} \int_{0}^{s^{2}} \cos \left(s^{3}\right) d t d s \) 71 answer -
Use logarithmic differentiation to find \( \mathrm{y}^{\prime} \). \[ y=\frac{\sqrt{1-7 x}\left(x^{2}+9\right)^{2}}{x^{2}+7 x+7} \] \[ y^{\prime}= \]1 answer -
\( \iint_{D} x d A \), donde \( D \) es la región en el primer cuadrante localizada entre las circunferencias \( x^{2}+y^{2}=4 \) y \( x^{2}+y^{2}=2 x \)1 answer -
Encuentre la masa y el centro de masa \( D \) está acotada por las parábolas \( y=x^{2} \) y \( x=y^{2} \); \( \rho(x, y)=\sqrt{x} \)0 answers -
Find all the second partial derivatives. \[ f(x, y)=x^{9} y^{8}+5 x^{4} y \] \( f_{x x}(x, y)= \) \[ f_{x y}(x, y)= \] \( f_{y x}(x, y)= \) \( f_{y y}(x, y)= \)1 answer -
Evaluate \( \iiint_{E}(x+y-5 z) d V \) where \( E=\left\{(x, y, z) \mid-5 \leq y \leq 0,0 \leq x \leq y, 0 \leq z \leq x+y^{2}\right\} \)1 answer -
k value
Determine all possible value(s) of \( k \) such that \( f^{\prime}(1)=5 \) if \( f(x)=\frac{x+k}{x^{2}-2} \)1 answer -
\( y^{\prime \prime}+3 y^{\prime}+2 y=\delta(t-5)+u_{10}(t) ; \quad y(0)=0, \quad y^{\prime}(0)=1 / 2 \)1 answer