Find the power series representation of the following functions 3x (a) f(x) = 2x+7

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A: This question is based on implicit differentiation.

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A: Given: vector valued function r(t)=<t, t2, t3>To Find: curvature at t=1

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A: (9)

Q: Rewrite the following equation with the variables separated. 3√t + y² dy = 6 dt o y² dy = (6 + 3√t)…

A: Please see the below picture for detailed solution.

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A: In this question we have to sketch the function as per the given statement.

Q: Question 1 [3 a) { exact: 1: Verify that the differential equation is (cos(x)+2x + y)dx+(−…

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Q: 3. Evaluate the definite integral below: S¯¼ √x² + 2x − 5dx + Sq − √x² + 2x − 5dx

A: To solve the following integral problem

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Q: Definite integral

A: Given :Definite integral

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Here, the given curves are: y=1+2x, y=2+x2

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Q: 1. f√√x²dx 2. Jdx 3. (2x + 3)² dx (4x²–5x+6) 4. S x² 3 5. f ( t + 1)²³ dt S dx

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Q: S Construct a table and find the indicated limit. x³ + 343 x+7 lim X→-7 x³ +343 X+7 lim X→-7 =

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Q: 4. The process of finding a general formula for the slope of a line tangent to a certain curve is…

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Q: sint F(x) = √"* ( *ª*** ( √ ¹ + uª) du) dt Jo

A: The Fundamental Theorem of Calculus says: F(x)=∫ag(x)f(t) dt⇒F'(x)=f(g(x))g'(x)

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Q: onsider the following. w=x^2/y ,  x=t^2 ,  y=t+1 ,  t=3 (a) Find d2w/dt2 using the appropriate…

A: Given :w=x2yx=t2  y=t+1t=3

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Q: • You will not receive credit if you submit your assignment late. P 1. ( Find the center, foci, and…

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A: Description given below with example

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Q: Find aw/as and ow/ot using the appropriate Chain Rule. Function Values w = y³ - 7x²y x = e³, y = et…

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Q: At how many points do the curves r₁(t) = ((t + 1)², — t² − 2t, t+2) and r₂(t) = (1 – t², t, t) -…

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Q: x) = = ph f and T3 on the same screen. y 2+ -1.0 -1.0 -0.5 -0.5 1 -1 -2 -3 y 2+ 2 1 -1 -2 -3 0.5 0.5…

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Q: Select the correct steps when differentiating from first principles. O a. O b. O C. O d. lim 0+x lim…

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A: We have to find out interval of convergence

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Q: F8 e³ti+cos(5t)j +3sin(5t)k 3 -i+cos(5t)j +3sin(5t)k Question 7 The position vector r(t) =…

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Q: 3) Determine whether or not the following 3D vector fields are conservative: a) (y²-z³)i + (2xy +…

A: As per the company rules we are supposed to answer only the first question and rest can be reposted.

Q: What is the general solution to y² tan(x) dy = sin(x) dx o y = √3 sin(x) + C o y = -√√3 cos(x) + C o…

A: Here we have to solve the differential equation.

Q: Function: w = y3 - 3x2y, x = es, y = et Point: s = 2, t = 2 Find del w/del s and del w / del t using…

A: If w=f(x,y) and x=g(s) and y=h(t) then,          ∂w∂s =∂w∂x.∂x∂s+∂w∂y.∂y∂sand         ∂w∂t…

Q: 16. Write an equation for the transformation of f(x) = |x| shown in the graph below. V

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Q: 4. Graph this piecewise function: f(x): = x+1 -2x-3 x<-2 xM-2

A: We need to graph the given functionf(x)=x+1x&lt;-2-2x-3x≥-2

Q: √5-x² LIL -√5 Jo 0 5 I² +2² (x+y) dy dz da

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Q: ind the definito integral that will computo for the area of the region bounded by y-2 ln x v-0 andy…

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Q: Let D be the planar region bounded by y = 0, y = x², and x = 1. The integral ff cos(z² + y²) dA…

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Q: Find the critical points of the given function. a) f(x)=√x²-4 b) f(x)= |3x +21-1

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