IV. Find Do not simplify your answers. dy dx 1 1. cos x + y² = x coshy - 2y, where x > 0

Q: 2. (D² + 3D + 2)y= 1+ 3x + x²

A:

Q: [₁x³√x² + 3dx x-3 2

A:

Q: √ 1 x²√2x-x² dx = x+¹√ √√2x-x² + c 3x²

A:

Q: Describe the end behavior (long run behavior) of f(x) = 28 As → →→ ∞, f(x)→ ? As I→ ∞, f(x) → ? v

A: This question can be solved using the concept of limits.

Q: -2/√√/3 dx x√√x²-1 • [²/²2 (x + 12/²3). dx sin² π/6 28. • √2 30.

A:

Q: Find an equation of the surface of revolution by revolving the plane curve 3y = √(9- [(x-1)] ^2)…

A: We need to identify the quadratic surface.

Q: rπ/4 x² dx (x²+4)5/2 (Use trigonometric substitution)

A: To evaluate the given definite integral.

Q: 21. 5₁ 1 dx (A) 2 So to dx dx both diverge when p = xP (B) 1 © DO dx and (E) -1 HOR LAY A DUPA

A: Divergent

Q: 19. -π/2 21. -π/4 23. [³5e* dx sin 0 de cos x dx sec² 0 do (2x secx tan x) dx 20. rπ/3 22. 24. [¹-dx

A:

Q: Find an equation of the surface of revolution by revolving the plane curve 3y = √(9- [(x-1)] ^2)…

A:

Q: mposition =

A:

Q: Identify the surface in the xyz coordinate system given by the equation: z=-√(4-y^2) O cylinder O…

A: Let's find.

Q: trigonometric substitution, what is f √x²-9 x3 sec ¹(-₁)-² + C √x²_9 2x² sec 6 ¹(-)- √x²_9 2.x² + C…

A:

Q: 1. ) cos (4) COS -π/2 f/² sin (1) sin (²) dx (Consider initially the first 2 terms)

A:

Q: Find u v, uu, |v||2, (u v)v, and u. (3v). . u = 8i + j - 3k, v = i - 4j + 3k (a) u. V (b) u. U (c)…

A: This question is related to vectors, we will solve it using given information.

Q: 7. Do as indicated. 1 1. Let f(x)= = Find the equation of the tangent line to the graph of f'(x) at…

A: This question is related to straight lines, we will solve it using given information.

Q: 20 x³ dx (x²+4)5/2 (Use trigonometric substitution)

A:

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 1+ 3 1. lim x12x² + x1

A:

Q: (A) = and B = . Find the vector projection of A D onto 2A - BO O O none of the above

A:

Q: Consider the quadratic function f(z) - 2² +0z + 4. Determine the following: (enter all numerical…

A:

Q: π/4 x² dx (x²+4)5/2 0 (Use trigonometric substitution)

A: Given integral I=∫0π4  x3(x2+4)52 dx

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 1+ 1. lim. 2-12x²+x-1

A:

Q: 6x5-25x+8x3+43x²-8x-12 4. Find (3x+-11x² +9x²-11x+6) (9x²+12x+16) -dx if this can be reduced to 63…

A:

Q: Solve the following differential equations of y"+7y' +10y=2e³x

A:

Q: Determine the order of the given differential equation and state whether the equation is linear or…

A: Here we have to determine the order of the given differential equation and state whether the…

Q: if any. Find the absolute extremum point (s) of f(x) = el-cosa on [-, ],

A:

Q: Find the limit. NOTE: Enter the answer using round brackets. t² +4 1 = lim t→+∞0 (?, ?) 4t² +5't

A: limt→∞t2+44t2+5, 1t

Q: f(x,y) = 3x-2y R: the circle x² + y²

A:

Q: 4. The integration da can be solved by using the 2+-2 ³+1 ♦ (Choose the correct letter). ²+2-2 A…

A:

Q: Calculuate the length of the curvey = 4√2 3 3|2 within the interval of 0≤x≤ 1,

A:

Q: 61. det t sectdt d 62. du Jo Ix/dx 0 px [Hint: Use Definition 5.5.3(b).]

A:

Q: x²+x+1 so Ja 2x²+2+x²+x dx dx = [Aƒ (x) – B ln(g(x))] à + D fb +2 and if A=,B<0, then g(x) = .

A:

Q: Find Do not simplify your answers. dy da 1. log;(√2x² + y) + tan(x² − 7") = sin¯'¹(x² − 1) + ½

A:

Q: /² sin sin ( π/4 x² dx (x²+4)5/2 (Use trigonometric substitution) fe2x+Inx² sin x² dx = = Find f…

A:

Q: 17. 2x√/x dx 18. de xVx S

A:

Q: Find the volumes for the following solids whose heights are defined by Z(x,y) and bases are the…

A:

Q: 3. S 2 x²+a² x4 = _ (x² + a²) ³² 3a²x3 -dx = + c

A:

Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, ....…

A:

Q: 15x²x³43x - 19 The integral (x + 1)²(x² - 6x +13) Ax + B What is the value of x²+bx+ca -dx? 3 A…

A: This is a problem related to integration. Based on the concept of partial fraction decomposition we…

Q: 12 || ti + t²j||dt = |

A:

Q: Using trigonometric substitution, what is √x²-9dx ? f x3 A sec (-) √x²_9 6x² +C B ¹ (1) - V +C (ⒸC)…

A:

Q: -2 + อน Ore 0

A: Suppose uxy=0 , denotes u = uy implies uy = 0 uxy = F(x) + G(y)  ,satisfies uxy = 0 a) y du/dxdy +…

Q: x+1 1-x In [cosh (x+1) + sinh (x+1) lim 2tanh x=1- lim_ In x=1+ l

A:

Q: The IBP formula fudv=uv-fvdu Which of the following statements fits and satisfies the equations? can…

A:

Q: (D4 − 1)y = 0

A: D4-1y=0

Q: d Calculate dt [ri(t) · r₂(t)] and [ri(t) × r₂(t)] first by differentiating . dt the product…

A:

Q: 2. lim (√x²-x-√x² + x)

A:

Q: d (h) (cot ¹(2)) = d (i)=(sec ¹(1))= = d (j) (csc-¹(2)) = dr 1 du 1+² dz 1 du I√²-1 dz 1 du I√²-1 dr

A: Given problem:-

Q: Question 10 > Put a dot on the vertex of the parabola below. What is the coordinates of the vertex?…

A:

Q: Determine the values of r for which the given differential equation has solutions of the form y =…

A: