10 End of block exercise: Pase 1002 find a solution: general solution of the differential equation x² dy dx = 2y + yx

Q: (I) Find the critical points of the function f(x) = x + x² + 1

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Q: Q5: Find the sums of the following (geometric series): 3n-1 1 6n-1 n=1

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Q: Given the function f(x) = x² + Draw a sketch of the graph of f. 16 - X x>0

A: Follow the procedure given below.

Q: Solve the following differential equations of -0 -(x² + y²)dx + (2xy + cos y) dy 2rud

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Q: Find a vector perpendicular to the 2-space line: Qx - Ny + R = 0

A: Please see the below picture for detailed solution.

Q: Find y = f(x), given d²y dx² = f'(x) = 2* In 2 + 2ex -x-² +2

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Q: X (X+2)5 d x

A: Explanation of the answer is as follows

Q: Find the maximum rate of change of the function f(x, y) 3y5 x at the point (3,4)

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Q: Coffee is draining from a conical filter into a cylindrical coffeepot at the rate of 10 in./min.…

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Q: Minimize c = 8x + y subject to 10x + 20y ≥ 100 0.8x + 0.1y ≥ 2 x ≥ 0, y ≥ 0

A: minimize c=8x+ysbuject to constraint10x+20y≥1000.8x+0.1y≥2x≥0, y≥0

Q: 35/ SEX √ 2 X-I d x

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Q: All Solve the following by L apace transformy" + 4y' + 3y = 0 ,y(0) = 3 y'(0) = 1

A: Given :y''+4y'+3y=0 y(0)=3 and y'(0)=1

Q: Find the area bounded by the given curves, or as described. I.) Sketch the graph II.) Find the…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

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Q: Which of the following statement is TRUE? (i) If Σα o an = and bn = then Στο bn n=0 2 an 3 (ii) If…

A: Solution is given below:

Q: ate of change of S is directly proportional to S(x), where S(0) = 10 and S(4) = 40 k, the…

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Q: If the Wronskian W of f and g is t²e5t, and if f(t) = t, find g(t). NOTE: Use c as an arbitrary…

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Q: Starting at age 35, you deposit $2000 a year into an IRA account for retirement. Treat the yearly…

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Q: claurin series for the given function. e² - e- 3 2 lor series generated by the function f

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Q: Evaluate the indefinite integral. -3.5 - 15t - 3t-¹)dt (-15-35-3t-1)dt = 1 4 +²√t - 2 In t+c (Type…

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Q: Evaluate the integral. 1 √2√2 ²² √2-4° dt t³

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Q: Find the area bounded by the given curves, or as described. I. Sketch the graph II. Find the…

A: Given: x= y2 + 4y, x=0

Q: Evaluate. 7u [(e70 +4u) du (eu +4u) du = (Type (Type an exact answer.)

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Q: Solve:  9 d2y/dx2 - 24 dy/dx +16y = 0;  y(0)=3, y'(0)=3 Write the letter corresponding to your…

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Q: Write and evaluate the definite integral that represents the area of the surface generated by…

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Q: 1. Find the derivative of the following sin² x cos² x a)y + 1+cotx 1+tan x

A: We have to find derivative of given trigonometric term.

Q: Part 2. Find the Standard Equation 3. hyperbola with vertices at (-2,-4), (-2, 6), foci at (-2,-5),…

A: Given,  Vertices: (-2, -4), (-2,6), Foci: (-2, -5), (-2, 7)

Q: The base of a three-dimensional figure is bound by the graph x = sin(y) + 1 on the interval [0, π].…

A: We have to find the area of each triangle.

Q: The base of a three-dimensional figure is bound by the line y = -x + 3 on the interval [-1, 1].…

A: Here, the cross-section is perpendicular to the x-axis. Therefore, the area is a function os x.

Q: Q1: Solve integral the following: 1- fx.√x-8dx 2- sin 2xdx

A: 1.∫x.x-8 dx2.∫0π4sin2x dx

Q: determine the average rate of chnage for the funcation f(x)=4log(x^2)+ 2/x betweem x=3 and x=5

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Q: Find the absolute minimum and absolute maximum of the function f(x) = (x2 − 1)3 defined on the…

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Q: The point (-1,-4) lies on the circle whose center is at (3,-1). Write the standard form of the…

A: As per our guidelines we are supposed to answer only one question. Kindly re-post other question as…

Q: 5) Find all values of x for which En=1 nxn (n+1)(2x+1)n converges absolutely.

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Q: . Given 1 [(5x+ + = + 1) dx a. ) Evaluate the indefinite integral above b. Evaluate the integral…

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Q: 3. (0.002x4 -0.3x² + 4x - 7) dx

A: We need to find,   ∫-1010(0.002x4-0.3x2+4x-7)dx

Q: 03: Evaluate the following integrals: (5) √cotx.csc4 x dx

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Q: Write out the form of the partial fraction decomposition of the function (as in this example). Do…

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Q: 8. Given f(x)=x+3 and g(x)=4 – x², find g(f(x)) and f(g(x)). 9. Given f(x)=x²+4x-9 and g(x)=-4x² –…

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Q: . foci: (±4,0) major axis of length: 1

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Q: Find the points on the cone z² = x² + y² that are closest to the point (-5,4,0)

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Q: Epa is investing $2500 at 6% per annum, with interest compounded continuously. She wants to come up…

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Q: IF x=t, y=t², 2= 2/3 t3 and r is the position vector, denoted by r=ti + t²j + 3/23 t²³³ k dT @ Find:…

A: Acccording to question,Given equations,x = ty = t2andz = 23t3andr = t i^ + t2 j^ +  23t3 k^

Q: Solve the following differential equations of 1 xy'dx + (x³y² +1) dy=0

A: We will use substitution x2=z. The formula I used has been written at the end of paper.

Q: 3. (1+2x − ¹) dx (assume x > 0)

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Q: alla Find xy² R2² -dA, R= [0, 4] × [ - 2,2] x² +1

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Q: 24\x² dy_ (xy + y²) dx = o

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Q: Determine the critical points of f(x) = 8x3+81x2−42x−8.

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Q: 06: a: Let A = Find (2A-I)B' 3 0 11 0 1 2 -1 1 5 =[₁ B = -2 0 3 2

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Q: Part One. All of the equations listed below are general equations of conic sections. Study each…

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