Evaluate the integral. NOTE: Enter the exact answer. 1 X for fo (ory + 173 dy d 1)² dy dx =

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A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: •√ (2x + √₁ (2r+√16-r²) dr by interpreting it in terms of areas. 10. Evaluate

A: Bh

Q: I'm not understanding what the answer is here? 77 and 71? Because that is not correct.

A: A rectangular page is to contain 76 square inches of print. The margins on each side are 1 inch. To…

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Q: Use the given graph of f(x) to find the intervals on which f'(x) > 0. Q 25- 20- 15- 10- 5- 64…

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Q: a) [ Sketch the region R. 1 b) [] Set up the double integral that represents the area of the region…

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Q: 3) A) E B) [ Consider the homogeneous DE: y'"" + 2y" + y = 0 Verify that y = cos(x) is a solution of…

A: The given differential equation is;  y''''+2y''+y=0

Q: c²e-2x³ dx [ +C

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Q: Find the derivative. F'(x) if F(x)= (ex² -3) ² F'(x)=

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Q: t exactly two of the labeled points in the figure below, which shows a function f, the derivative f'…

A: Disclaimer:  “Since you have posted a question with multiple sub-parts, we will solve the first…

Q: The directional derivative of f(x, y) = e²y - x at the point (1, 2) in the direction indicated by…

A: In this question, We want to find the directional derivative in the given direction.

Q: Find the derivative. F'(x) if F(x)= (ex¹ +5) 3 F'(x)=

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Q: Find f'(x) if f(x) = -7x5 +4√x. f'(x) =

A: To find derivative f'(x)

Q: SPA 32 Select one: True ● False dx dy = 13 2

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Q: Use a double integral to find the EXACT area enclosed by the graph of r = 3+3 cos 0. 8=1/2

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Q: Let →r(t)=⟨2t−3,5e^−2t,−2e^2t⟩ Find the line (L) tangent to →r(t)r→(t) t=-3.

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Q: 2 -2 [ 3x² + 4y dy dx = [[ 3x² + 4y' dx dy. We have Select one: True False

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Q: please both

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Q: 1. Integrate using an appropriate method. [2si 2 sin³(r) cos² (r)dr

A: The given integral is: I=∫2sin3xcos2xdx   As we know that; The trigonometric identity; sin2x+cos2x=1…

Q: 10. Solve 3log x= log 512-log 8

A: To slove 3logx=log512-log8

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Q: III-Déterminer la dérivée de : a) f(x) = lnx lnx + 1 III- Determine the derivative of: ex +1 J b)…

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Q: Find Ay and f'(x) Ax for the given function. 13) y = f(x) = x + x2, x = 8, and Ax = 0.05

A: Q13)

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Q: The directional derivative of f(x, y) = xe + 2y at point (2, 0) in the direction of the angle = is:…

A: Given that fx,y=xey+2y at the point 2,0 and θ=π3 find the directional derivative

Q: Consider vector field: F = e i-cos y j+ sin² z k. Obtain divergence and curl for F at points (0,,).

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Q: Current Attempt in Progress Evaluate the integral by applying the following theorems and the power…

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Q: Use a double integral to find the volume of the indicated solid. X 2 N z = e¯(x+y)/4 2 0≤x≤ ∞o 0 ≤ y…

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Q: Use partial fractions to find the power series of the function: 8 n=0 11x² + 629 (x² + 64)(x² + 49)

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Q: Find an equation for the hyperbola that satisfies the given conditions. Asymptotes: y = x, hyperbola…

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Q: dx Assume that x = x(t) and y = y(t). Let y = x² +5 and dt dy Find when x = 1. dt (Simplify your…

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Q: 8. Graph the curve and find the area that it enclosed: r = 2 cos(0).

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Q: Find a polar equation for the curve represented by the given Cartesian equation. (Assume 0 ≤ 0 <…

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Q: 1a) Convert the Cartesian equation (x^2 +y^2-1)^2 +4y^2-1 = 0 to polar coordinates. 1b) Use a…

A: By using the following substitution we can convert the Cartesian equation to polar form. x²+y²=r²…

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Q: (e) Determine whether the following series converges or diverges by using the comparison test: Σ 1=0

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Q: Find the lim inf (xn) and lim sup (xn) of Xn = √1 + n² 2n - 5

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Q: Find the angle between the vectors in radians and in degrees. (Round your answer for part (a) to…

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Q: 2. If y is the solution of the initial value problem = 3(y - 1)(y-2) with y(1) = 3, what is lim…

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Q: Show that the function has removable discontinuity at the origin sin 2x 2x f(x) = 1 if x = 0 if x =…

A: Given that a function f(x) and we show that the function has removable discontinuity at the origin .…