4. 4 1 [x²ydxdy 20

Q: Solve the given differential equation by undetermined coefficients. y" + 5y = -180x²e5x y(x) =

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Q: Q6A)If y = cos ¹) prove Zyy + z = 0.

A: See this solution in below

Q: Evalute ff Rx²dA, where R is the region in the first quadrant bounded by the hyperbola xy = 16 and…

A: The given integral: ∫∫Rx2dAWhere R is the region in the first quadrant bounded by the hyperbola…

Q: 3x 9. fxdx A.ln(e6x + 1) + c ₂-6x + c 3x c.exe Barctan (e6x) + c D.†arctan(e3x) + c

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Q: 5: Find the volume of the solid which is generated by rotating the region bounded by y=√x, y=x-2 and…

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Q: Consider the function f(x) below. Over what open interval(s) is the function decreasing and concave…

A: We need to find out the intervals on which the function is decreasing and also concave up.

Q: Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20…

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Q: B. A rock is vertically thrown upward from the surface of the moon at a velocity of 24 m/sec. 2 The…

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Q: Evaluate the integral using the indicated trigonometric substitution Select the correct answer. 044…

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Q: Find the points on the graph of the function that are closest to the given point. f(x) = x², (0,4)…

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Q: (a) Use the Midpoint Rule with n = 6 to approximate integral 8 x-6 S8 dx 6 x+8 ?

A: As per the instruction, we will be answering the first question. Given:

Q: the open interval(s) on which the curve given by the vector-valued function is smooth. (Enter your…

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Q: A - [4 = 2 5 5 c=[-³3 C - 1 3 2 3] 0 - 2 1 B = D= 1 5 6 1 0 - 8 2 - 4 1 5 0 - - 3 1 2

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Q: Question 1 Let a = 2i - 3j + 2k and b = i - 2j - k. a) Determine whether the vectors a and b are…

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Q: Sketch the space curve represented by the vector-valued function and give the orientation of the…

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Q: Find d [f₁z²dA where R = {(x, y) | 36x² +16y² ≤ 576}

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Q: As per the trigonometric substitution x = sin(0), the following triangle is obtained. cos(0) Submit…

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Q: Consider the following information fz(x, y) = 2x³ - 2xy and fy(x, y) = 6 - x² - y². Use the Second…

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Q: 7. The points of inflection are found by solving the first derivative equal to zero. 8. When the…

A: You must have idea about Calculus in order to get the answer for these questions.

Q: The masses m, are located at the points P₁. Find the moments Mx and My and the center of mass of the…

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Q: A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles…

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Q: 4 Determine -2 u tv and Give a is i and v и So Keat orthogonal to ²-5²³ lutô| = |a²|+12²1…

A: Given the vectors u+v and u-v are orthogonal and  u+v=u+v To find u and v .

Q: Apply the rule of integration by parts. -S Sudv. dv = uv - du = Let dv= ew dw and integrate the…

A: Here we will fill all blacks of prat 2 as shown below

Q: Determine the location and value of the absolute extreme values of f on the given​ interval, if they…

A: To determine the location and value of the absolute extreme values of f on the given interval, if…

Q: 4. √ (4x²–5x+6) dx

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Q: Use the Root Test to determine whether the series convergent or divergent. Identify an 00 n = 1 מס →…

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Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

A: Here we have to find the volume.

Q: Complete the proof of Property 4 of the following theorem by supplying the justification for each…

A: We have to complete the proof of property 4.

Q: 2x et. Vi-eza ex fer.

A: ∫ ex1-e2xdx=∫1-u2du=∫1+cos2v2dv=12·∫ 1+cos2vdv=12∫…

Q: Determine the location and value of the absolute extreme values of f on the given​ interval, if they…

A: The function is given as , fx=8x33+14x2-16x find the location and value of the absolute extreme…

Q: The resistance R of a copper wire at temperature T = 25 °C is R = 18 22. Estimate the resistance at…

A: Let's solve.

Q: 11. inverse Laplace transform of (a) F(s) = (b) F(s) = (c) F(s) = (d) F(s) = 3 8² +4 4 (8 - 1)³ 2s +…

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Q: Do the first two terms of the Taylor series by hand where X_0 = 1

A: Given :∫1232xe-xdx

Q: 19. For a given function, f(r)=³-152² +48x+2. (a) Find the interval(s) on which is increasing. (b)…

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Q: Drag and drop your answer into the box: (a) An antidervative of f(x) is = 4x4 + 2x² - 5 (b) The…

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Q: eliminate the arbitraty constats of the differential equation y = C1e^2x + C2xe^2x a. y” + 2y’ + y =…

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Q: Use the first derivative test to find the location of all local extrema in the interval (0, 4) for…

A: The given function is f(x)=-5x+3 ln(x)

Q: Solve the given differential equation by undetermined coefficients. y" - 8y' + 20y = 100x² - 65xex…

A: The characteristics equation is  m2-8m+20=0⇒m=4+2i, m=4-2i So, the general solution to the…

Q: The four figures below are graphs of the vector-valued function r(t) = 8 cos ti + 8 sin tj + (t/8)k.…

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Q: The area enclosed by the curve y² = x(1-x) is given by .

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Q: 28 Find nd [² [ 2h f f(4x)dx if f(x)dx = 5. 16 Enter the exact answer. [fe f(4x)dx =

A: Given :∫1628f(x)dx=5

Q: S tanx secx dx

A: We have to evaluate the given integration.

Q: (C) (In Mpg) for a certain vehicle can be approximated by m (x) = -0.03x +2.645x-35.029, where x is…

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Q: 36. What is the area of the region bounded by the graph of y = 3x - 4, the y-axis, the lines y = 1…

A: See the details solution in below

Q: A cylindrical can is to be made to hold 1 litre of oil. Find the dimensions which will minimize the…

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Q: Problem 4. A particle moves back and forth along a straight line with a velocity of v(t) = 1-²…

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Q: lim 0-4 In[(1 + h)² + 1] - ln(2) y

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Q: Step 5 Let x = sin(0). Differentiate with respect to x on both sides. dx = Rewrite the integral by…

A: We need to fill in the blank.

Q: Verify that the function satisfies the three hypotheses of Roll's Theorem on the given interval.…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Solve differential equation dx -(2ln5y+x-¹) 2xy-1

A: Solution is given below: