Problem3 Find a curve in the xy-plane passing through the point (1, 2) and for which the normal line at any point (x, y) has slope -xy².

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A: Integrate the integrand (x2-x+12)/(x3+2x) .

Q: Q2 a) Find the derivative using logarithmic differentiation. x³(2x - 1) (5r+1)7(r+1)

A: topic- derivative of a function Note: As per bartleby guidelines, we are supposed to solve only…

Q: * The differential equation 2ydx-(3y-2x)dy=0 is Exact homogenous and linear Exact and linear but not…

A: The answer is given below:

Q: Find the value of ff xye**y dxdy (solve) (yeye)(xex - e*) Option 2 O yev (xe* -ex) Option 1 (yeyev)…

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Q: Let a = (5, 5, - 3) and b = ( – 5, 3, 0). Find the projection of b onto a. proj¡ b = <

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Q: Find the indefinite integral. (Use c for the constant of integration.) [ (42³1 + (4t³i + 14tj…

A: We need to find integral.

Q: Locate the stationary point of the function z = 3x² + 4xy + 3y² (solve) Saddle point Maximum point O…

A: To locate the stationary point of the given function.

Q: The vectors u = (5, -4,0) and v = (-4,-5, 4) are orthogonal. Select one: O True O False

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Q: 1 2 1 Q2. If A = 200 31 2 find A¹.

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Q: A B 3-5 In Ix-31+ C X --5 In Ix-31 + C x3 3x²+5 (x-3) S: C dx x3+5 In Ix-31+ C D x3 +5 In Ix-31+ C

A: Evaluating the indefinite integral

Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

A: Topic = Series

Q: Find the area of the surface generated when the given curve is revolved about the given axis. 1 3 y…

A: y=8x13, for 0≤x≤18, about y-axis

Q: Use the information given below to find sin (a-ß). 12 5 12 tana= with a in quadrant III cos ß= 13 I…

A: Find sin(alpha-bita)   When tan(alpha)= 12/5 in third quadrant  And cos(bita) = 12/13 in first…

Q: Let a = 5j + k and b - 27 + 3 + 2k. Find - 3ā – 36.

A: We can find the given vectors.

Q: 08 06 04- 02- }} ye y=0x=y² 02 yer* dxdy = 36 38

A: To switch the order of integration and then evaluate the value of integration.

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: We have to analyze and sketch a graph of the function and find any intercepts, relative extrema,…

Q: (6xy - 3y² + 2y)dx + 2(x − y)dy = 0; when x = 0, y = 2

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Q: If v=3i+2j+ k,w=3i+ 4k and the angle between v and w is 90, find v.w (solve) 10 8 0 O Option 3 O

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Q: Write the given expression as an algebraic expression in x. sin(2 tan-¹(x)) X

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Q: B: if Z-4x²-8xy +7y5-3 then find Z, Zy, Zxx, Zyy

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Q: Set R be the region defined by √2² +²³² ≤4 and let f(z,y) = 1²-22+ y². Find the global maximum and…

A: The region R given is: x2+y2≤4y≥x

Q: Consider the following infinite series. Complete parts (a) through (c). Σ 310.1) k=1 a. Find the…

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Q: Find dy if the curve is described by the equation x³ 4x³y + 3y² +Ske y

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Q: x²5 - - 5y = x + 1 is non-homogeneous second order differential equations dy² with constant…

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Q: Let A(t)=15(0.8)^0.2t (in milligrams) be the amount of drug in a patients body at time where t is…

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Q: Find all solutions to the equation. tan 0-1=0 Write your answer in radians in terms of , and use the…

A: The objective is to find all the solutions.

Q: The general solution of the DE+4-5y=0 y= Ae* + Be5x Option 2 O y = Ae* + Be-5x y= Ae* + Be-5x Option…

A: We have to find the general solution.

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

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Q: Find the Riemann sum using R4 over the interval [0, π]. y = x² sin x

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Q: Let f(x) = { 2x-3. 3x²+2, if x < 3 if x ≥ 3 be a piecewise function. Evaluate Sof 0 f(x)dx=

A: We can find the integration of the piecewise function as below.

Q: Evaluate 2 1 ² ₁² + √²³² - ²3/7 + 3x²³ - ²/3 d. X =)dx 3 X X 2 6.780 6.870 -6.870 -6.087 -0.687…

A: Given ∫12x3+x43-3x32+3x2-2xdx

Q: Find an equation of the plane. The plane through the point (6, −8, −8) and parallel to the plane…

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Q: Evaluate 3 [²^{²} + √x² − ² + ³x² − ²) dx = x None of them 21.466 2.1664 -2.1646 -21.664 21.664…

A: Given problem:-

Q: a.) S (t² – 9) (4 – t²) dt from 2 to 3 b.) fx dx from 1 to 2 c.) f (x² - d.) f sin 0 de from 0 to…

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Q: (a) [1 Show that the following equation represents a sphere, and find its center and radius. x² + y²…

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: Translate into English:  a. ∀x(E(x) ⇾ E(x + 2)).  b. ∀x∃y(sin(x) =y).  c. ∀y∃x(sin(x) = y).  d.…

A: Solution : Given that to translate into English

Q: Find the sum of the series: n=0 2-1 (-1)"64"- n!

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Q: Find the volume of the parallelepiped determined by the vectors a (3, 4, 1), b = (0, 2, 4), = (2, 4,…

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Q: Let a = (-4, 5, -2) and 6=(-1,0, 4). Find à x b.

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Q: Switch the order of integration of the following integrals, then evaluate: ƒ ƒ x sin(y²) dydx = x=0…

A: Explained below

Q: A furniture store sells 96 coffee tables per month at $1100 each. The owners estimate that for each…

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Q: totals the proportion of observations that are less than or equal to the class at which you are…

A: Solution given below

Q: Find the Maclaurin series of xe³x. Σ n=0

A: Find the maclaurin series of x9e3x.

Q: The length of the cross product between the vectors j and -j is equal to the zero vector. Select…

A: Solutions

Q: 1) Evaluate the following iterated integral. 2/2 sin(2y) SS dydx y 0x

A: Use change of order of integration.

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

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Q: Use the integral test to determine if series converges or diverges by solve Σ 11 ne 22 The series…

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Q: The Maclaurin series of the function f(x) = 6x²e-4² can be written as f(1) = Σ₂² n=0 where the first…

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Q: The Eigen value of matrix p is (solve) ГО 0 Lo 1 0 0 1 -3 -4] (0,-1,-3) O (0,2,3) O (0,1,3) O…

A: This question can be solved using the concept of matrices and determinants.

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = e−x/2,  x…

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