Use integration by parts to find the indefinite integral. (Use C for the constant of integration. Remember to use absolute values where appropriate.) [in (√x² - 9) dx

Q: r(t) = (-3√√9-1²,4 sin (4t), 2 In (-3-2t)), then the domain of r is given by the interval Select…

A: Here, r(t)=-39-t2, 4sin(4t), 2ln(-3-2t)

Q: Find f" (x), given f(x) = sec x. O f" (x) = sec³ x tan x Of" (x) = sec a tanz Of" (x) = sec³ x + sec…

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Q: In(t³ + 1) + t³ + 1 r(t) = 4: then the limit lim r(t) equals 1-0 -i-(4e-²¹-5e²¹)j- - sin³t -k, 13

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Q: 11 1 2 (x-3)/3 -dx

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Q: The domain of the function f(x, y) = 3xy 2+√4x2+y2-16 is:

A: Given problem:- fx,y=3xy2+4x2+y2-16  To find:- Domain of f(x,y)

Q: Work Problem 1( Let z=(y-x)³, and as(1 t) and y = st². Use the chain rule to compute da and da da

A: Given problem:- Here  z=(y-x)3  And x=s(1-t), y=st2  find using chain rule zs and zt

Q: After successfully passing the Technical Written Examinations, you're now at the PRC Main Office ta…

A: Given: there are 5 registrations specialist on different windows faciltaiting registrations, the…

Q: The following limit Select one: O O equals 16 3 equals 0. None of them O does not exist. O equals 3…

A: This question is based on two variable limits.

Q: Find the limit, if it exists, or show that the limit does not exist. x² - 3y² lim (x,y) (0,0) x² +…

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Q: Integrate: S (2x2-10x+15) gở ba tô 2x + 3 ln() + C ○ 3 ln()+ +C O 2x+3 ln()+ ○ 3 ln() + C +C dx

A: ∫(2x2-10x+15)x2-5x+6dx=∫(2x2-10x+12+3)x2-5x+6dx ∫2(x2-5x+6)(x2-5x+6)dx+∫3(x2-5x+6)dx…

Q: 5. (x² + y² + 1)dx - 2xydy = 0

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Q: 8. Find the first two non-zero terms of the Taylor expansion for function f(x)=sin x and a given…

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Q: Suppose that the yield (measured in kg/ ha) of an agricultural crop is represented by the function…

A: We need to find rate.

Q: a. b. dx x+2x³ In S is Inx In 2x² + 1| + C X C √ √2x² + 1 + ₁ C. d. In|2x² + 1 1 + C In x + In|2x² +…

A: Given problem:-

Q: The area bounded by the x-axis, y = x², and y = 2 - x.

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Q: 4. Graph the equation: f(x): = 1, -2x + 4, -2, -3≤x≤0 0 ≤ x ≤ 3. x > 3 -1 5+ 44 3- 2+ +1 -1- -24 -3-…

A: This is a graph of piece wise function

Q: Determine any planes that are parallel or identical. (Select all that apply.) OP₁: -60x + 90y + 120z…

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Q: 9. The equation of the graph of the shaded region below is most likely to be Im A. |z − 4 + i| ≥ 2√3…

A: The objective of the question is choose the correct option for the region.

Q: Choose the correct answer for the following limit: Select one: Ο Α. 0 O B. Does not exist. OC. None…

A: According to question,Given Limit,Let l = limx, y→0, 0x3 + 6y25x3 + y2

Q: 4 Use the substitution z +9=u² to evaluate √√+9

A: Note: Since, the student has asked to solve only question no. 4, so we are solving accordingly…

Q: 5. The angle between the tangent line and the normal line is (a) 180° (b) 90° (c) 45° 6. If x= 3t-2…

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Q: For the curve f(x) = Find the horizontal and vertical asymptotes. x-4x² +2 x² - 4x +4

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Q: lim t→∞ 14/3 + 71/3 2 (6+²/3 +11) ²

A: To find out the limit.

Q: (4x² - 9)72 99

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Q: A y=1 x=y² B y=x² C (1, 1) X=1 X (0,0) Region A is bounded by the parabola x = y², the line y = 1,…

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Q: a) Find the integral / r(t)dt. b) Find parametric equations for the tangent line to the given curve…

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Q: is

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Q: Find dy dr dy dr for y = ㅇ 2 5+ 6t dt.

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Q: Let f(x) = 2x+1, if x1 O (-∞, 1) U (1,00) O (-∞0, 1] U (1, ∞0) OR O (-∞0, 1) U [1,00)

A: topic- limits and continuity

Q: z = (x + y)², x = s²t, y = st². Use the Chain rule to find dz for t = 1 and s = 2. ds

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Q: Given the system x + 3y = 10 2x - y = 6 a) Create the augmented matrix of the given system b) solve…

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Q: 4. Evaluate (²52³Vl-Pax

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Q: For the limit, lim (x,y)→(0,0) sin(x² - y²) x² - y² if we approach along y-axis, we will get 1.…

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Q: For the piecewise defined function None of these 2 what should be the value of c so that we have…

A: In this question we have to find the value of c so that f(x) is left continuous at x=1

Q: 1 x xy 14. JJ j dz dy dx 0x²0

A: We can find the value of the integral.

Q: dz Evaluate: 5 10+2% 0 1 O Divergent 00 0-1 15

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Q: (z In z + 5)dz

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Q: If the equation z=squarerootx^2+y^2 equals the spherical equation phi=c, what is the angle of…

A: The given problem is solved below in detail.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Given that point 2,6,-8   and vector or line ,n=jTo  find : equation of plane Solution :Direction of…

Q: I dx x√x² - 64

A: we will solve integration by substitution.

Q: Evaluate et +2e2t-et e2t +1 dt.

A: Given that a integration problem and we solve this problem by using general property of integration.…

Q: What is the integral of f sin² x cos²x dx? O cos(z) sin³ (2) cos(z) sin(z) + 4 4 O sin(4x)+4z 32 +C…

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Q: Question An equation of the plane passing through A (1, -1, -1), B (1,0,2), and C (-1,-1,-5) is:…

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Q: Determine the indefinite integral below. S(9x+4)²dx. (9x+4)²dx =

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Q: Which of the following is the partial derivative with respect to x of the function f(x, y)= 4xy + 7x…

A: Given problem:- f(x, y) =4xy+7x+6y-ln(9xy)   To find :- fx(x, y)

Q: Determine whether the lines L₁ and L₂ are parallel, skew or intersecting L₁: x = 4 + 2t, y = -5 +…

A: L1 : x=a1+b1t , y =c1+d1t , z=e1+f1tL2 : x=a2+b2s, y =c2+d2s , z=e2+f2sthen Lines L1 and L2 are…

Q: 2. Solve the following 4th order linear differential equations using undetermined coefficients: y…

A: We need to solve D.E.

Q: Solve: x²y + 4xy' + 2y = 0 Indicial roots: r₁= General Solution: y = C₁ a.x-1 b. x3 c. xinx d. e3x…

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Q: Given the matrices A - 5 -5 2 2 2 - 2 and B - 4 2 -1 -2 5 0 A. It is Select an answer to multiply…

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Q: Use the limit definition of partial derivatives to find fx(x, y) and fy(x, y). f(x, y) = x2 − 5xy +…

A: We need to find partial derivative.