Find the equations of the lines tangent and normal to the curve guen by para- metric equations at + = 1/5. t 풍 x = 4 cost and y = 2 sin²t

Q: For F(x, y, z) = y²z³ i + 2xyz³ j + 3xy²z² k, determine whether or not the vector If it is…

A: Let's find.

Q: 32-37 FOURIER INTEGRALS AND TRANSFORMS Sketch the given function and represent it as indicated. If…

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Q: Evaluate [x²z dx - yx² dy + 7 dz along the curve C shown in the figure. с 4 X [x²zdx - yux²2 dy +7…

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Q: Find the integral of the following equation integrate cos(x + pi/3) dx

A: Given problem:- Find the integral of the following equation integrate cos(x + pi/3) dx

Q: Evaluate the line integral. [(x - y) ds C: x² + y² = 16 Lox (x - y) ds = C i

A: Evualate the line integral

Q: Solve for the solution of: (D2 - 4)y = 8e2x - 12

A: Given problem:- Solve for the solution of: (D2 - 4)y = 8e2x - 12

Q: Find the indefinite integral. (Use c for the constant of integration.) [ (41³ + 146) (4t³i + 14tj -…

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Q: A particle is moving with the given data. Find the position of the particle. a(t) = 2t + 9, S(0) =…

A: In this question we have to find the value of s(t).

Q: Find the arc length of the graph of NOTE: Enter the exact answer. L = r(t) = √²ti + e-√²tj + 2tk, 0≤…

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

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Q: C. Find the slope and the equation of the tangent line to the 21 21 = 3x al 28. y=x²-3x+3 at (3, 3)…

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Q: Describe the graph of the equation. r = 7costi 14 sin tj + k O An ellipse in the plane x = 1, center…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

A: To find the domain of the following vector‐valued function.rt=25-t2 i+t2 j-4t k

Q: Evaluate the vector-vall function at each giver r(t) = cos(t)i + 3 sin(t)j (a) r(0) = (b) г(π/4)=…

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Q: The revenue from the sale of a product is given by the function R=3000x-0.1x³ dollars. Use graphical…

A: Write an inequality to represent that revenue must be at least $39,960. 3000x-0.1x3-39,960≥0

Q: Use logarithmic differentiation to find dy/dx. y = (4 + x)5/x dy dx II

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Q: Sketch the region enclosed by the curves x = sin 3y and x = y, and compute its area as an integral.…

A: We have to find the area between the curves.

Q: Find the derivative of f(x) =de 22 Of(x) e (e-2x) ²-e -2x O f'(x)=x²e-2 (-2) O (E) None of these O…

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Q: Use Green's Theorem to evaluate the line integral Jo (y - x)dx + (2x - y)dy for the given path. C: x…

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Q: Evaluate (F JC Er F • dr. F(x, y) = xi + yj C: r(t) = (7t + 4)i + tj, 0≤t≤1

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Q: (D² - 3D + 2)y = 2e-* +8

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Q: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 6 P6(x) =

A: nth Maclaurin polynomial for the function :       Pn(x) =  ∑i=0n fi(0)i!xi = f(0)+f'(0)x + f''(0)…

Q: Find all solutions of the equation in the interval [0, 21). csc 0 7 3 If there is more than one…

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Q: 10. Given that y = at x = 1. e* X + 1 Find, in terms of e, the values of . 최 and dx dx²

A: (10). Given: y=exx+1   As we know that; The Power law; ddxxn=nxn-1 The Quotient rule;…

Q: Solve for the solution: d3y/dx3 - d2y/dx2 -dy/dx +y = 0

A: Solution is given below:

Q: (-3,0) y = h'(x) (0, -1) (-1,-2) (0, -2) (3,0)

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Q: Question 7 Given the function f(x) = 8 +5x², calculate the following values: f(a)= f(a+h)- =…

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. 11 ["||ti + 1²i||dt = |

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Q: r(t) = (t, In(t), √t), to = 1 e the equations for the line to approximate r(to + 0.1). to + 0.1) =

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Q: Find a general solution. Show the steps of derivation. Check your answer by substitution. -1.2 6. y'…

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Q: The smaller the curvature in the bend of a road, the faster a car can travel. Assume that the…

A: Given that the smaller the curvature in the bend of a road, the faster a car can travel.

Q: A company that sells memory chips for computers established the price-demand and cost functions as:…

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Q: lim x++∞ COS X log logi x

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Q: Solve the differential equation: * (D² + 1)y = tan x

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Q: 518 SHOW ALL WORK Aau aາq JV Find the exponential function given by f(x) = Ca that models the data…

A: f(x)=Caxf(0)=Ca02=CC=2Thereforef(x)=2axf(1)=2a16=2aa=3Thereforef(x)=2×3xCheck for x=2 and…

Q: Find r'(t), r"(t), r'(t) ・r(t), and r(t) × r"(t). r(t) = 2t2i - 2tj + 2 13배 (a) r'(t) (b) r"(t) (c)…

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Q: [₁ [6x² arcsin(x)]dx

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Q: d²y_dy + y = 0 dx d³y_d²y dx³ dx²

A: Auxillary equation ism3-m2-m+1=0m2(m-1)-(m-1)=0(m2-1)(m-1)=0(m+1)(m-1)(m-1)=0m=-1.1.1  are the roots

Q: Express the limit as a definite integral on the given interval. n lim [7(x)³ - 5x;*]4x, [2,7] n→∞ =…

A: Here, the limit of the integral is [2, 7]. Further, ∆x is replaced by dx and replace xi* by x. Thus,…

Q: Determine whether F(x, y) = 6x²y i+ 4xy²j is a conservative vector field. If so, find a potential…

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Q: Evaluate the following indefinite integrals using integration by trigonometric substitution.…

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Q: Determine the sum of the following series. 31 10 Σ(1)

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Q: - y' + y = 2 sinx when y(0) = -1

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: f(x) = 2x + 3 x 1 1 ; a = 1

A: limx→1+f(x)=limx→1+x2+2                =12+2=3limx→1+f(x)=3

Q: 3. Find if y³ + 2xy - x² = cos x using implicit differentiation.

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Q: Which statement is true? There are many anti-derivatives, f(x), of a function g(x). There is only…

A: Given

Q: Consider the following function. f(x) = 4x2/3 Find f(-8) and f(8). f(-8) = f(8) = Find all values c…

A: Here, the given function is: f(x)=4-x23

Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

A: Given problem:- Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to…