Calculus Archive: Questions from December 23, 2023
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2. \( \lim _{(x)} \frac{2 x^{2}+2 y^{2}}{\sin \left(x^{2}+y^{2}-\pi\right)}= \) ? (a) -2 (b) \( -\frac{1}{2} \) (c) 0 (d) 2 (e) The limit does not exist. 3. If \( f(x, y)=e^{x y} \ln y \), then \( y \1 answer -
3. If \( f(x, y)=e^{x y} \ln y \), then \( y \frac{\partial f}{\partial y}-x \frac{\partial f}{\partial x}= \) ? (a) \( \frac{e^{x y}}{y} \) (b) \( (y-x) e^{x y} \ln y+e^{x y} \) (c) 0 (d) \( e^{x y}1 answer -
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22. If ( rac{d y}{d x}=rac{y}{x}(x>0, y>0) ) and ( y=3 ) when ( x=1 ), then (A) ( x^{2}+y^{2}=10 ) (B) ( y=x+ln 3 ) (C) ( y^{2}-x^{2}=8 ) (D) ( y=3 x ) (E) ( y^{2}-3 x^{2}=6 )
22. If \( \frac{d y}{d x}=\frac{y}{x}(x>0, y>0) \) and \( y=3 \) when \( x=1 \), then (A) \( x^{2}+y^{2}=10 \) (B) \( y=x+\ln 3 \) (C) \( y^{2}-x^{2}=8 \) (D) \( y=3 x \) (IE) \( y^{2}-3 x^{2}=6 \)1 answer -
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