I. Solve the following integrals completely and honestly. Show your solution in ink and as neatly as possible. No solutions means incorrect. 1. (√sinx+cosx) dx 2. [sin'x cos³x dx 3. [√tanx sec'x dx Stan'7x dx 4.

Q: 6 By separation of variables, Solve the following 5 PDES :- учи ²4 dx2 0 o u(e,t) = u(5,t) =6 u(x,0)…

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Q: 2. Evaluate the double integral that will find the volume of a solid bounded by 21-2y²-322 and the…

A: Given: z=1-2y^2-3x^2 and xy-plane

Q: Evaluate the line integral y dx + xy dy where C' is the rectangle with vertices (0,0), (5,0), (5,4),…

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Q: Determine the roots of y"" - 4y" + 3y = 0

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Q: Find the area of the region enclosed by the curves y =

A: answer is in next  step

Q: For the following exercises, use the second derivative test to identify any critical points and…

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Q: Consider the Initial Value Problem (IVP) given by dy dr y (0) = 1. a. Sketch the slope field of the…

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Q: X = 2t-2 - y = ln(t³) Which integral gives the arc length of the curve over the interval from t = 2…

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Q: S- tanh e cosh(z) – sinh(z) -dz

A: Let's evaluate given integral.

Q: Marksberg radially has a population density of 1000e^−0.01r2 people per km^2, where r is the radius…

A: Here we have to find the population within 5km.

Q: By direct partial integration, Solve the following PDES 8- 82u = COSX COSYSXUCX,t) Ex u(π, y) = 2…

A: Given ; del2u/delx del y=cosxcosy.

Q: show that V(x, y) = x 'f (2x+y) is the general Solution of av X du 2X 1 = V ду dax

A: Explanation of the answer is as follows

Q: 4 Find the area of the region bounded by x = 2y²+1 and the y-axis using the horizontal strip.

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Q: Determine the general solution of y" - y = 0 given y₁(x) = e e-2x using reduction of order

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Q: Given a second order differential equation dx X = e³t dt where t = 0, x = 2. 3t Using Laplace…

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Q: / If y" + 2y' F5y = e-Sint, y(0) = 0, y' (0) = 1

A: We solve the given differential equation using the higher order LDE techniques.

Q: Evaluate the following * [: 2x(4x² – 3)³dx (4x²-3)6 +C 24 O (4x² - 3)-6 24 +C (4x²-3)6 24 O " (4x² -…

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Q: Solve the given differential equation. All solutions should be found. dyx³ 8y dx X NOTE: Use c for…

A: As we know that; The standard form of 1st linear order differential equation is: dydx+Pxy=Qx So, the…

Q: A large pond initially contains 200 liters of fresh water (no chemical). A fluid containing 10 grams…

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Q: aluate the line integral y dx + xy dy where C is the rectangle with vert 0), (5, 4), and (0,4).

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Q: I. 4. Evaluate each determinant. 2 -5 2 -1 4

A: We have to find out determinant

Q: 4 x dx Y 3- SSin X

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Q: = 10. Find a second-degree polynomial P such that P(1) = 7, P'(1) = 7, and P"(1) P(x) = Need Help?…

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Q: 6 By Separation of variables, Solve the following 5 PDES :- ²4. ²4 0 o 2 dt² dx² u(e,t) = u(5,t) =6…

A: Given

Q: Derivative of arctan(ln(n))

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Q: answer

A: We will solve the problem.

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: To find the volume of the solid that results when the shaded region is revolved about the indicated…

Q: show that V(x,y) = x 'f (2x+y) is the general Solution of : x av dx 2x du 1 = V ay

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Q: 5) y = tanx secx 6) Y = b x+1

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Q: Find the solution of the given initial value problem in explicit form. π sin(2x) dx + cos(9y) dy =…

A: Given: Now,                sin(2x)dx+cos(9y)dy=0Integrating both sides we…

Q: 5.) I. -2 -3 -6 2 Simplify. Write "undefined -4 6 0 +

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Q: Find the area of the region bounded by the curves y = sqrtx and y = −x^2 between x = 0 and x = 1.…

A: Here we have to find the area of a region.

Q: 2 убличк In'/xl alx

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Q: 2. Solve for x. 45x-x² = 4-6 a. b. (1 − x)5 = (2x − 1)5 - 60 c. 55 = 1+5e-0.6x d. 3 log x + 10 =…

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Q: (x²-y²)²1 Evaluate: ₁²² du du dt x+y

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Q: 3. The definition of Antiderivative states that A. A function (x) is called an antiderivative of the…

A: 3. The antiderivative of a function f(x) is a function whose derivative is equal to f(x).

Q: 8. The value of ve A. sin-1 (e) + C C. sin-1 (e-x) + C dx B. -sin-1 (e-2x) + C D. sin-1 (e-2x) + C

A: Topic = Integration Correct option = A

Q: San 4h (x) dx = [ -3 y h 8 2 AN -3 10 4 -1/ -7 -7 7 x

A: From the graph, note that: ∫-30h(x) dx=-1 because area bounded by the curve h(x) is -1 in -3 to 0.

Q: Find the slope of the tangent to the curve y = 3e^(2x) at (0,3)  a. 3  b. 2  c. 6  d. 12

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Q: f(x) = x - 3, g(x) = x² Find (f + g)(x). 2 - (f + g)(x) = x+x-3 Find the domain of (f + g)(x).…

A: It is given that f(x) = x-3 g(x) = x2 We need to find the solution to the given questions.

Q: +∞ (x²+4)3/2 dx

A: To find: Integration

Q: 2. The Substitution Method states that A. If F'(x) = f(x), then [ f(u(x))u' (x) dx = F(u(x)) + C B.…

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Q: Evaluate: ³₁₂₁(4x²y — z³) dz dy dx

A: The given integral is  ∫-13 ∫-24 ∫10 4x2y-z3dz dy dx

Q: Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable…

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Q: Water is flowing into a conical vessel 18cm deep and having a diameter of 10cm across the top. If…

A: We have to find the rate of volume.

Q: 1. Given vector 2 0-3 is 2. It is known that a à vector : ( 2 ) and 3 = (-1) is a vector in 1R³ with…

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Q: Set up but do not evaluate an integral that represents the volume of the solid of revolution 2x + 1…

A: Given:   y = 2x + 1      y = ( x - 1 )2

Q: Solve the given differential equation. All solutions should be found. (5y¹ + 2x³y) dx − (4xy³ + x¹)…

A: Using integrating factor make equation exact

Q: Consider the parametric curve: X = sin² (t) y = -9t Which integral gives the arc length of the curve…

A: Topic = Integration

Q: Which integral gives the arc length of the curve over the interval from t = a to t = b?

A: This is a problem related to integration. Based on the general formula of length of arc we will…