a. (7+7i)(i + 1) UNA 7+7i i+1 C. (727°) (121°) e b.

Q: S 1 xvx²-2x dx = √x²-2x X +C

A: To prove that ∫1xx2-2xdx=x2-2xx+C

Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…

A:

Q: Question 9 Using trigonometric substitution to solve: cos x dx f 3 (4-sin²x)2

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Q: Determine whether the sequence a₁ = find the limit. Show All Your Work! 1+9n² 1+n² converges or…

A: To determine whether the given sequence converges or diverges.

Q: VI. Suppose h' is continuous at x = 0 and h'(x) =tan(2x) - 1 if x > 0. Find h(0), if it exists.

A: Let's find.

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: 2. Specify on which intervals is f increasing/decreasing and where the graph of f is concave…

A: First derivative test: If the first derivative of the function is positive over an interval, then,…

Q: Determine the values of r for which the differential equation y' +9y = 0 has solutions of the form y…

A: Given differential equation.

Q: An object moving along a horizontal coordinate line has directed distance s(t) = 4t³ +9t² - 30t + 5…

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Q: 19. TT/2 -π/2 sin 0 de 20. * sec² 0 de

A: 19 ∫-π/2π/2 sinθdθ [-cosθ ]-π/2π/2 0 - 0 =0 other way sin is odd function so also integration is = 0…

Q: Identify the center of the conic section whose equation is 4x 2 - 25y 2 - 8x - 100y - 196 = 0. (-1,…

A: We can identify the center as below.

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

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Q: If what does the following integral equal? -2 p(u)du = | - 4 3 p(u)du = 4 and p(u)du = 8.3 - 4 3

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Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 6 in.…

A: A box with a square base and no top is to be made from a square piece of cardboard by cutting 6 in.…

Q: Consider the partial differential equation u, + uux = 7+ uxx: Determine the order of this equation;…

A: Given differential equation:- ut +uux =7+uxx

Q: 15x² x3-43x - 19 - (x + 1)²(x² - 6x +13) Ax + B S ax²+bx+c The integral What is the value of dx can…

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. - 3. lim 1-3 (x − 3)…

A: limx→0 sin xx =1   and   limx→0 tanxx=1.

Q: dy II. Find Do not simplify your answers. da 1. log3 (√2x² + y) + tan(x - 7") = sin ¹1 (x²-1) +

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Q: 31. (a) 32. (a) 33. (a) 12x-1| dx √2 + x) dx e* - 1| dx L'i lex -3π/4 (b) cos x dx (b) [*/² | } −…

A: Given: ∫-11ex-1dx

Q: log(x+3) z-1-1-cosh(cos-12) 4. lim

A: Given,            limx→1-log12x+31-coshcos-1x

Q: log: (x+3) 2-1-1-cosh(cos-¹x) 4. lim

A:

Q: Find the area of the region bounded by    x2 = 4 - y    and     y = x -2  Hint: use Vertical strip.

A:

Q: our answers.

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Q: 31. (a) |2x - 1| dx (b) 3π/4 1.T CT/2 \cos x dx

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Q: 19 Give the properties for the equation 9x 2 + 16y 2 - 36x + 96y + 36 = 0 Major Axis 8 16 9

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Q: The IBP formula fudv-uv- - fvdu can also be written as fudv + ſ vdu = uv Which of the following…

A: Given that the four options  To find choose the correct option which is satisfi IBP formula

Q: Let w = x³y cos(5z). Find the following. (a) g(x, y, z) = дw (b) Əy(x, y, z) = ду (c) o (x, y, z)…

A: Given data÷

Q: Solve the following differential equations of y" +4y'+3y=3e²x;

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Q: (A) = and (B) = . Find 2A - BO* none of the above

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Q: Integrating Factor by Inspection: 9. (x4y+)dx + xy³dy = 0

A: Let the differential equation is of the form Mx, y dx + Nx, y dy = 0  ...........(1) If Mx+Ny≠0 and…

Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…

A:

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

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Q: dy II. Find Do not simplify your answers. dx ㅠ 1. log;(√2æ² + y) + tan(xª — πª) = sin¯¹(x² − 1) + ½…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Find the most general form of the antiderivative, F(x), of the function f(x) = −3√x - √√x. Provide…

A: Given fx=-3x5-x3 To find antiderivative (Integration)

Q: Determine whether the equation is exact. If it is exact, find the solution. If the differential…

A:

Q: Describe the long run behavior of f(p) = (p+ 2)(p+ 4) (p + 5): As p →→ ∞, f(p) → ? ✓ As poo, f(p) →…

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Q: (D4 − 1)y = 0

A: D4-1y=0

Q: Given : A B Ⓒ E b 27π²-24 [x³sin(2x) dx = . 64 2π 3 3π 4 TU 4 =|m 5 T 6 Find b if Isb -SOST

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Q: Integrating Factor by Linear Equations: dy 11.42 dx =

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Consider using the method of partial fractions to solve x²+x+1 Sa 2x²+2+x²+x A In(x²+1) B x+2 D…

A: This is a problem related to integration of the function using partial fraction decomposition. Based…

Q: Solve the given differential equation. All solutions should be found. (4y³ + 2x²y) dx - (3xy² + x³)…

A: Use the substitution method and solve the differential equation.

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

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Q: 49-52 Sketch the curve and find the total area between the curve and the given interval on the…

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Q: x²+x+1 Sa 2x²+2+3+x A B cb dx g(x) - dx = [Aƒ (x) − B ln(g(x)] + D fb da, and if A = ‚B <0, then dx…

A:

Q: Integrating Factor by Inspection: 5. (xy-2y²)dx - (x²-3xy)dy = 0

A: (xy-2y2)dx-(x2-3xy) dy=0x(y dx-x dy)-2y2 dx +3xy dy=0dividing by xy2;(ydx-x dy)y2-2x dx +3y…

Q: dy II. Find Do not simplify your answers. dr 2. y= tan ¹(coshr) (sin²x) (sech x)secz S [use…

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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: Let f(x) = 31² - 20x + 25 2x² + 12 - 1 This function has: 1) A y-intercept at the point 2)…

A: Given that    f(x) = (3x2-20x+25)/(2x2+1x-1)

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

A:

Q: Q2) Which of the following series is converge or diverge Σ{"} ,0.7777777777777 n=1 . Σ n=1 27

A: a)=∑n=1∞ n-1n2=∑n=1∞ 1n-1n2{using p-series test:∑n=1∞ 1np converges only when p&gt;1diverges for…