Calculus Archive: Questions from April 03, 2023
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What is the dy/dx for the functions 229, 233, 235?
For the following exercises, find \( \frac{d y}{d x} \) for each function. 228. \( y=\left(3 x^{2}+3 x-1\right)^{4} \) 229. \( y=(5-2 x)^{-2} \) 230. \( y=\cos ^{3}(\pi x) \) 231. \( y=\left(2 x^{3}-x2 answers -
\[ \begin{array}{l|c|c} y=f(g(x)) & u=g(x) & y=\boldsymbol{f}(u) \\ \hline y=8 \tan \left(\pi x^{3}\right) & u=1 & y=8 \tan u \end{array} \] Need Help?2 answers -
Differentiate the function. \[ g(x)=3 x^{-3}\left(x^{4}-3 x^{3}+13 x-2\right) \] \[ g^{\prime}(x)= \]2 answers -
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Verify the identity. \[ \frac{(\sin (x)+\cos (x))^{2}}{\sin ^{2}(x)-\cos ^{2}(x)}=\frac{\sin ^{2}(x)-\cos ^{2}(x)}{(\sin (x)-\cos (x))^{2}} \]2 answers -
Which of the following functions is continuous at (0, 0)? (i) f (x, y) = { x4 y4 x4 + 6y6 if (x, y) ≠ (0, 0) 0 if (x, y) = (0, 0) (ii) g(x, y) = { x y x2 + 2y2
Problem \# 6: Which of the following functions is continuous at \( (0,0) \) ? (i) \( f(x, y)=\left\{\begin{array}{ll}\frac{x^{4} y^{4}}{x^{4}+6 y^{6}} & \text { if }(x, y) \neq(0,0) \\ 0 & \text { if2 answers -
Find proj \( _{b} \mathrm{a} \). \[ \mathbf{a}=-\mathbf{i}-5 \mathbf{j}+6 \mathbf{k}, \quad \mathbf{b}=6 \mathbf{i}-3 \mathbf{j}-2 \mathbf{k} \]2 answers -
Evaluate the double integral I = ∫ ∫ D ( xy^2 + 3x^2y ) dA when D = { (x, y) : 0 ≤ y ≤ 1, −y ≤ x ≤ y2 answers
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Find \( f \) if \( \operatorname{grad} f=\left(y z e^{x y z}+z^{3} \cos \left(x z^{3}\right)\right) \vec{i}+x z e^{x y z} \vec{j}+\left(x y e^{x y z}+3 x z^{2} \cos \left(x z^{3}\right)\right) \vec{k}2 answers -
Solve the initial value problem for \( y(t) \). \[ y^{\prime \prime \prime}+4 y^{\prime \prime}+y^{\prime}-6 y=-12 \] \[ y(0)=1, y^{\prime}(0)=4, y^{\prime \prime}(0)=-2 \] \[ Y(s)= \] \[ y(t)= \]0 answers -
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18. \( \int_{1}^{3}(3 x-1)^{3} d x \) 20. \( \int_{0}^{1} \frac{2 x}{x^{2}-3} d x \) 22. \( \int_{0}^{3} x(x-3)^{2} d x \) 24. \( \int_{0}^{\infty} e^{-x} d x \)2 answers -
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5) Partial derivative. Compute \( f_{x y x z y} \) for \[ f(x, y, z)=y \sin (x z) \sin (x+z)+\left(x+z^{2}\right) \tan y+x \tan \left(\frac{z+z^{-1}}{y-y^{-1}}\right) \]2 answers -
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4. [-/5 Points \( ] \) DETAILS \[ \begin{array}{l} \int x^{2} \sqrt{4-x^{2}} d x= \\ 2 \sin ^{-1}\left(\frac{x}{2}\right)+\frac{x \sqrt{4-x^{2}}}{4}+C \\ \sin ^{-1}\left(\frac{x}{2}\right)+\frac{x\lef2 answers -
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Demuestre d/dx [sex x] = sec x tan x usando la regla del cociente y las identidades trigonométricas.0 answers
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