Calculus Archive: Questions from July 24, 2022
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1 answer
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\( \int_{0}^{\pi / 4} \int_{3}^{6}(y \cos x+3) d y d x \) \( \int_{3}^{7} \int_{3}^{9} x y e^{x+y} d y d x \)3 answers -
2. Solve the given initial-value problems. (a) \( y^{\prime \prime \prime}+2 y^{\prime \prime}-5 y^{\prime}-6 y=0, \quad y(0)=0, y^{\prime}(0)=0, y^{\prime \prime}(0)=1 \) (b) \( y^{\prime \prime \pri1 answer -
4 answers
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Prove the following identities a) \( \frac{\sin (\alpha+\beta)}{\sin (\alpha)+\cos (\beta)}=\frac{1+\cot (\alpha) \tan (\beta)}{\sec (\beta)+\operatorname{cosec}(\alpha)} \) b) \( \frac{\sin (3 \theta1 answer -
1 answer
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1 answer
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Q. Suppose Dy \( y=N_{0} e^{k \tau} \) ه) find 1\( ) y= \) ? 2) if \( \tau=2 \) then, \( y= \) ? \( \pi \)1 answer -
please solve
11. Differentiate. a) \( y=\left(2 x^{2}-1\right)^{3}\left(x^{4}+3\right)^{5} \) b) \( f(x)=\frac{6 x+5}{\sqrt{7-3 x^{2}}} \) c) \( y=\sin \left(x^{3}\right) \cos ^{3} x \) d) \( h(x)=\frac{x^{2}}{e^{1 answer -
15,37 only please.
In Problems 1-18 solve each differential equation by variation of parameters. 1. \( y^{\prime \prime}+y=\sec x \) 2. \( y^{\prime \prime}+y=\tan x \) 3. \( y^{\prime \prime}+y=\sin x \) 4. \( y^{\prim1 answer -
1 answer
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Sketch the graph of a twice-differentiable function \( y=f(x) \) with the properties given in the table. Choose the correct graph below.1 answer -
Find the total differential for the function \( w=13 z^{3} y \sin x \). \( d w=26 z^{3} y \sin x d x+13 z^{3} \sin x d y+39 z^{2} y \sin x d z \) \( d w=13 z^{3} y \sin x d x-13 z^{3} \sin x d y-26 z^3 answers -
Given \( f(x, y)=x^{3}-2 x y^{5}-4 y^{2} \) \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \end{array} \]1 answer -
1 answer
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3 answers
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3 answers