Find the MacLaurin series for the function f(x) = (1 + x)7. It is actually finite – it’s a polynomial. Write out the polynomial in the usual way that you write polynomials.

Q: 3x-4 1. Y= Arctan 4

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Q: (2х — Зу + 1)dх — (3х + 2у — 4)dy %3D 0

A: We have to solve the differential equations.

Q: Given: -8 17 sine =

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Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

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Q: S2(x* +1)e** dx . -5x t³ -9 -dt . 2t +3

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Q: 1. Two sides of a triangle are 15 and 20 ft long, respectively. a) How fast is the third side…

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Q: 2. Determine whether the following integral is convergent or divergent. Do not guess! 4 dx x2 – x -…

A: To determine whether the following integral is convergent or divergent.∫04dxx2-x-2

Q: 7. Two functions are defined as f (x) and g (x) = where x * 1. a) Find f (x) g (x). Simplify your…

A: We can solve the given question as follows:

Q: Find the general solution of the given DE (x-3y-1)dx-(x-3y+5)dy%3D0.

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Q: 34. f (г) — 1 ; с34

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Q: If f (z, y) — е"у, then fr (1, In (3)) —??? (а) е (b) e³ (с) 1/3 (а) 3 (е) 3ln (3)

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Q: How 3 Find the absalutemaximes and minima far the funCtion (4x-x) Cosy an the rectangular plate…

A: Solution is given below:

Q: Find the general solution: dy = tanxtanydx %3D

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Q: Using an appropriate lineař appratimation, Feel free to leave fractions in answer.

A: The given approximation 35

Q: 3 2 2 3 1, find the matrix B Such that AB = 5 3 4 3 4 2 1 6 1 5 6 4 , If A = 1

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Q: Find the derivative using the definition 2х-3 y = 3x-2 What is the solution if the answer is: 2х-3…

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Q: Suppose we have f (x, y) = x + 1' What is the level curve for f (x, y) = 5 ? (a) a parabola (b) a…

A: Let's find.

Q: (2х — Зу + 1)dх — (3х + 2у — 4)dy 3D0

A: The given DE is of the type: Mdx+Ndy=0 where  M=2x-3y+1 & N=-(3x+2y-4)⇒My=-3, Nx=-3⇒My=Nx

Q: e® +e¯® –x² –2 sin² x–x² x→0

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Q: 4)Given f(x) = 2x/(x2 + 1) a)Find the derivative. b)Find the critical numbers .

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Q: 5.(Straightforward) Make the differential equation below exact by find- ing an integrating factor…

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Q: 1. Which of the following is the solution to the equation below? cos? æ + 3 cos a – 4 = 0 x = 1+…

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Q: When the price of a certain commodity is p dollars per unit, the manufacturer is willing to supply x…

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Q: e*+e¯& =x² –2 lim sin² x–x² x→0

A: Given limx→0ex+e-x-x2-2sin2x-x2 If we put x=0, we get a solution of the form 00…

Q: 1 dx so that the integral evaluates to - 3x2 integral / Ae2*- 2x³ – 3x² Replace the letter A in the…

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Q: 2. Y' = csc - y cot x ans. y sin x = x + C %3D

A: We know that; The standard form of the linear differential equation of first order is: dydx+Py=Q ;…

Q: 12. f (x) = xe -x

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Q: Bx Bんt2

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Q: Learning Task 2: Find the derivative of 4x2 + 6y³ = 50 by filling the blanks. %3D (2 x)(x²-)…

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Q: (sinx)" dx is:- 4) The solution of (sin x) dx A) (sinx)' dx B) C) Zero

A: ∫0πsinx7dx=∫0πsin7xdxWe know…

Q: oup Discussion Problem: Figure 3-8n shows the graph of y = 2 + (x - 1) sin e function has a…

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Q: Answer the following about the function f (x) = (1/3)x^3 − (1/2)x^2 −2x + 1 a. Find all critical…

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Q: if xo = 2, x1= 3 and x2 = 4 the second degree %3D %3D polynomial for f(x) = ! using Lagrange %3D…

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Q: Wheat is poured through a chute at the rate of 10 ft/min and falls in a canonical pile whose bottom…

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Q: Derive the derivative function for secx and express your answer in product form.

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Q: Given: -8 17 cose = 15/17 -8/17 8/17 -15/17

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Q: Solve the differential equation: dx+(x-y+2)^2dy=0

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Q: a. x² + y² = x +y b. x² +xy³ = x c. y = sec(x +y)

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Consider the following planes. 3x + 2y - z = 42 x - 4y + 2z = 0 (a) Find the angle between the two…

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Q: 3. Determine the values of a, b, and c such that the function f(x)=x+ax + bx+c has a y-intercept of…

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Q: 2Tx [e?n* + 23c] dx

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Q: Find the mass of the solid bounded by the ry-plane, yz-plane, xz-plane, and the plane (z/3) + (y/4)…

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Q: メ-1dx

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Q: e one Choose one e in the same plan

A: We have to choose one lie in the same plane or not

Q: 1と 8t y=x?+4 ソニx? ー4 4

A: The region is bounded by the curves y=x2+4 and y=x2 from x=-4 to x=4revolved about x-axis

Q: (a) Differentiate f(x) = Vx+4 by using the first principle. (b) Differentiate the following…

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Q: Suppose the position of a particle is given by parametric equations x(t) = t3-2 and y(t) = 4t2. (a)…

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Q: - ydy (y + 1) - J y + 1

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Q: 4 1 4. |x2ydxdy 2 0

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Q: Evaluate this path limit: 4.ry3 lim (z, y)¬(0, 0) 2x² + y6 I=y% =???

A: To find: Limit of the function of two variable along the given path.