Advanced Math Archive: Questions from August 02, 2022
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\( \iiint_{B}\left(z \sin x+y^{2}\right) d V, \quad \) where \( B=\{(x, y, z) \mid 0 \leq x \leq \pi, 0 \leq y \leq 1,-1 \leq z \leq 2\} \)3 answers -
3 answers
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(9) One of the following is set of linearly dependent functions: A) \( \left\{\frac{1}{3} e^{x}, 3 e^{2 x}\right\} \) B) \( \{3 \sin (2 x), 2 \sin x \cos x\} \) C) \( \left\{x^{2}+x, 2 x(x+1)\right\}1 answer -
If \( x^{y}=y^{x} \) and \( x=2 y \), then the values of \( x \) and \( y \) are \( (x, y>0) \) (A) \( x=4, y=2 \) (B) \( x=3, y=2 \) (C) \( x=1, y=1 \) (D) None of these1 answer -
2. The graphs of \( y=f(x) \) and \( y=g(x) \) are shown. Using the graphs, evaluate a) \( f(1) \) c) \( f(4)-g(-2) \) b) \( g(-2) \) d) \( x \) when \( f(x)=-3 \)1 answer -
double integral
(1 point) Evaluate the double integral \( \iint_{R} 2 \sin (6 x-y) d A= \) where \( R=\{(x, y) \mid 0 \leq x \leq \pi / 2,0 \leq y \leq \pi / 2\} \)1 answer -
Initial-Value Problems Determine the solutions of the IVPs of Problems \( 41-52 . \) 42. \( y^{\prime \prime}+4 y^{\prime}+4 y=t e^{-t} \), \( y(0)=-1, \quad y^{\prime}(0)=1 \) 44. \( y^{\prime \pri3 answers -
1 answer