Given the differential equation xy³dx + (x²y² + 1) dy = 0, What is SN dx ?

Q: Find the area of the shaded region. f(x) = 10x - 3x²-x³, g(x) = 0 The area is (Type an integer or a…

A: This question can be solved using the concept of  area bounded by two curves.

Q: scost 2.) Find the derivative: 1 (t) = (sin" (t²), e² ² lnt>

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Q: Q1/ Find the derivative of the following functions: where x>0,x #1 a- y = x** x√√2x+1 b- y = exsin…

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Q: 1. y=(sin ¹x² + X 1+tan x

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Q: Q17) The slope of the tangent line of the curve x² + y²=5 at the point (1,-2)- A) √√4x-4-√√5x-1 x-3…

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Q: π Determine the Taylor series for f(x) = sin x about x == 3

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Q: Define the following sets: A = {1,3,7,9,10) B = C = {0,1,3,10} D = {2,4,6,8,10} E = {x: x is a…

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Q: Your are driving away from Tampa. Your distance (in miles) away from Tampa x hours after 12:00 noon…

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Q: A line segment has (x₁, y₁) as one endpoint and (xm, Ym) as its midpoint. Find the other endpoint…

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Q: 5. r(x, y) = ln (x + y)

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Q: Use linear approximation, i.e. the tangent line, to approximate 101 as follows: Let f(x) = = and…

A: We need to find value using linear approximation.

Q: Use Taylor's Theorem to find an interval [ — z, z] where the Maclaurin polynomial p2(x) - = 1 1…

A: The given function is fx=cosx and Maclaurin polynomial p2x=1-x22. The Taylor's Theorem states:  If…

Q: stion T1_Q3 rove by contradiction that there are no positive integers p and q such that 4p²-q² = 25

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Q: Applications

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Q: Evaluate the following integral: * *π/2 [sin² 6 1/42 4 O - (2/63) O - (3/28) O 2/63 sin x cos³ x

A: The objective of the question is evaluate the definite integral and choose the correct option.

Q: so ne dx

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Q: Evaluate the given indefinite integral. 7 c 7 cos √6x dx= [ (Type an exact answer. Type an…

A: Solution: ∫7cos 6xdx Apply integration by parts

Q: f" (1) =

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Q: 10. f(x, y) = x/(x² + y²)

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Q: Find the derivative of the function using the chain rule. y = log10(7x)

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Q: dy 2.L/+R/+y=0 dx2 dx

A: Homogeneous Differential equation with constant coefficients.

Q: 4a) S 3x+7 (8+6x-9x²) 3/2 -dx 4b) S 2x²-11x-1 (x+3)(x² +1) -dx

A: ∫un du =un+1n+1+C ∫sec2(u) du = tan(u) +C Note : As per our guidelines ,we can solve first question.…

Q: 80 80 (20) If the graph of the function f(x) is stretched vertically by a factor 2 and then…

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Q: C(q) = q³ - 11q² +52q and R(q) = -3q² +2400q, what is the minimum marginal cost? Given Cost and…

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Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and ƒ'(0) = 8,…

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Q: 5. If A is (8, -7) and B is (5, 16), find a unit vector in the same direction as AB.

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Q: 4. [ε (8x − 3) (4x² – 3x) * dx

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Q: Compute the following limits, if possible. You may use L'Hospital's (Bernoulli's) rule if it…

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Q: Find the nth Maclaurin polynomial for the function. 4x - 5 f(x) n = 4 x + 1 P4(x) = =

A: The function is  f(x)=4x-5x+1

Q: For each of the questions below, indicate if the statement is true (T) or false (F). (a) Any…

A: answer  is next step . as per guideline i can only answer 3 question .

Q: DETERMINE WHETHER THE GIVEN FUNCTION n(x) IS CONTINUOUS OR DISCONTINUOUS AT x = 2 3x² +4 n(x) = if x…

A: For function to be continuous at any point, limiting value of function at that point must be equal…

Q: 2 n (2k + n)2 k=2

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Use Newton's binomial theorem to calculate √50 with 4 terms.

A: You have submitted multiple questions. According to Bartleby guidelines, I'll solve the first…

Q: Find the area of the surface obtained by rotating the curve Y = from x = 0 to x = 1 about the…

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Q: (2 fi = f(x²+xyz, y² +22= Prove that (y²-2x) ou 2ZX) then ne (²h-x) he 18

A: Concept: Partial derivative : The partial derivative is similar to the normal derivative except in…

Q: The rate in which the balance of an account that is increasing is given by A'(t)=375e^(0.025t).…

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Q: The graph shown below is f(x) = 2x 2 - 1. If g(x) = f(t)dt, find g'(3). X 543-2-1 1 2 3 4 5 -2 54 &…

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Q: its not 1

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Q: Find the nth Maclaurin polynomial for the function. f(x) = ex, n=5

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Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy²= 2 (C- cos x) O y…

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

Q: C. Find the volume of the solid generated by revolving the area bounded by the given curves about…

A: Let's find volume of solid.

Q: 6. S e3w dw 9-4e6w

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Q: The linearization at a = 0 to √8+7e is A + Ba. Compute A and B. A B= || ||

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Q: Solve the following matrix equation for a, b, c, and d. b b + c 2 [ad - [10²] = 3d + c 2a - 4d 11 6…

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Q: 1. 2y7y"+12y + 8y = 0

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Q: Question 7 AL Given that APOBDEA and APOCA are semicircles with centre O and P respectively. AP = 10…

A: We can solve the given question by the help of trigonometry.

Q: Show all steps carefully! Given two points A(1,1,1) and B(-7,9,2)find: a) The vector equation for…

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Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

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Q: Given ; = -5 cos 0 and r₂ = 5+5 cos 0 Sketch and then set up integral for area bounded by the…

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Q: Find the distance between the points. (−14, 1), (1, −7)                     units

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