Find dy dx for sin(xy) + y³ = x² + 1 and use it to find the equation of the tangent line at the point (0, 1)

Q: Q1: Find the general solution of the following first order D.Es a) (xy² + x)dbe+(a + y)dy =…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: From a group of 18 student representatives, 5 will be chosen to work on a fundraising committee. How…

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Q: Use gauss divergence theorem to calculate the the flow through a surface S that is immersed in a…

A: Concept: The formula for the divergence theorem: ∫∫SF→n^ds…

Q: Q.2)(A) Determine (215) ² Σ (5)(2+1) of each point convergens or diverges: 13.0

A: Given

Q: If y = (3 + 2x), what is y"? 00 48(3 + 2)2 © 12(3+2r)? O24(3 + 2)²

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Q: The equation (y-x)=x(dy/dx) is Bernouli (y^n> 1) O linear in x O Homogenous O variable separable

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Q: 6X-1 4X+1 X+7< 6 OX<-89/2 (-∞, - 89/2) O X<- 89 (00,- 89) O X<-2/89 (-∞, -2/89) O X<∞ (89/2, ∞) 8

A: x+7&lt;6x-14-4x+16x+7&lt;6(6x-1)-4(4x+1)4×6x+7&lt;36x-6-16x-424x+7&lt;20x-1024Multiply 24 on both…

Q: 2. find the derivative 725 - 2z² - 3z + 12 Enter your answer

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Q: Graph the function. Plot five points on the graph of the function: one point with x = 0, two points…

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Q: Q:1) Evaluate the line integral: [[xy'dx+x²ydy] C: [(x, y): x=t₁y=f²,0 ≤t≤1].

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Q: Find A-B using the following matrices: 5 6 1 2 9 3 A-3 5 8 B = 4 0 3 4 6 7 -5 -1 3

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Q: The slope of tangent lines to a curve y=f(x) is given by f'(x)=1/√√x +4x^3-1. If the point (1,6) is…

A: Equation of curve

Q: A car dealership has 4 red cars, 3 blue cars, and 2 silver cars to display in a line facing forward.…

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Q: Determine whether or not the following functions are continuous at (0,0). -1 for (x, y) = (0,0) a)…

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Q: Determine whether the series converges. O The series diverges. O The series converges. Σ k In(k + 4)

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Q: b- 2π -50 1 (1+tan²0)3 do

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Q: From a group of 18 student representatives, 5 will be chosen to work on a fundraising committee. How…

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Q: Find the general solution for the following Second Order Deferential Equation: d²y Q4: dx² - y = ex…

A: The given differential equation is;  d2y/dx2 -y=ex+x2.

Q: Find the minimum value of the following function: f(x,y,z) = x² + 2y² + z² - 2xy - 2y + 5  using…

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Q: Solve the differential equation. 12. ( r + sin θ – cos θ) dr + r ( sin θ + cos θ) dθ = 0

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Q: Based on the graphs of f(x) and g(x), what must the domain of (f. g)(x) be? 10 8 7 6 5 2 g(x) 1…

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Q: The following logarithmic expression, log2 (4), when completely simplified becomes

A: Given,  log2(4)x

Q: What is general solution of the given ODE. * dy = cos² (x − y + 1) dx cot (x-y+1) + x + 1 = C Option…

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Q: The graph of the function y = f(x) passes through the point (-1, 1) and the line tangent to the…

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Q: > Question 6 Let u and v be functions of and let u' and v' denote the derivatives of u ar (a) Dz…

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Q: Initially, there are 250 bacteria and after seven hours, 800 bacteria are observed in the culture.…

A: This is a problem related to differential equation. Based on the growth law we will answer the…

Q: Q2 (a) Sketch the following function of period 27. f(x)= |x| (-1 ≤ x <n) f(x + 2x) = f(x) (b)…

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Q: Evaluate the following integrals: 4T Vcsec 0 de 0

A: We need to do integration of our given function. Which we can do it as

Q: C. 1-3/5 (6x³+11x² - 4x) 18x² +22x-4) dx

A: We can solve this as follows:

Q: Question 17 D, (cos(sin x)) = O-sin(cos z) - sin + cos z COS I - sin(sin z) O sin(sin x)

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Q: Graph the parabola. y = (x+5)²+1 Plot five points on the parabola: the vertex, two points to the…

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Q: Solve for y + In lyl at x=6: y'=(yx^2 - y)/(y+1); y(3) = -1 4.5

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Q: Question 11 Evaluate the limit: lim h→0 Question Help: Video (-5+h)² - 25 h

A: We can solve this as follows:

Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = x and then find the nth Taylor…

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Q: X1 + 4 x2 + 3x3 = 2 2x16 x2 + 6x3 = -3 5x12x2 + 3x3 = -5

A: Given :2x1+4x2+3x3=22x1-6x2+6x3=-35x1-2x2+3x3=-5

Q: Q2: Find the following limits sin3y cot5y 3. lim y-0 ycot4y

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Q: Question 14 If z= f(t); u = g(x); x = h(z), which of the following is/are correct? du du dr dz (a)…

A: To find out the correct option.

Q: Find a value of n such that y= x" e satisfies the equation xy' = (x-6)- y. (Use symbolic notation…

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Q: Determine dy/dx, if the curve is described by the equation 4y^3-5x^2y=4x^2

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Q: An engineer working for Florida Power and Light has been given the task of enclosing a 72-m²…

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Q: (y³ - 3x²y + x³ - 4x) dx + (3xy2 - x³ + 8y³ +y + 5) dy = 0 I. f(x, y) = M(x, y) dx + g(y) II. Find…

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Q: Given the function z = f(x,y) = x²y + 2y² + 4xy-2, find the following: a) Find all of its critical…

A: Here, we need to find the critical points.

Q: The function is defined by f(x)=√x. Write down the expression for h (x).

A: Given: and f(x)=x.

Q: Which graph could be used to find the solution(s) to the system of equations y = log₂(x + 2) and…

A: The system of equations y=log2x+2 and y=x3-2x2-5x+6

Q: x. e²ydy + (*²*¹) dx = ( 0 (Variable separable)

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Q: (1) IF: a 21-j+ k, b=i+2j- 3k, č=-3i+2j+ k Find a.b, a.c, č.ā (a+b).(a-b),(ã+c).(ā-) (ã+2b-3c). (ā-…

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Q: Example (2): Find area shown in the figure bounded by (y = x²), (y = -x) and (x = 1).

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Q: Separable DE) y'ln² y + y√√x=0 y(0) = e

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Q: The domain of the logarithmic function y = log4 (x + 3) is Ox>0, XER Ox-3, x=R Oxz-3,TER OX>0, XER

A: Let's find domain of given logarithmic function.

Q: Find the direction angles of the vector. (Give your answers correct to 3 decimal places.) u = −3i +…

A: Topic = Vector