and

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: 15. Sketch y = f(x). Properties are: Max at P(2, 2) Mins at Q(4, -1), R(-1,2). Oblique asymptote y =…

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Q: The base of a certain solid is the area bounded above by the graph of y = f(x) = 4 and below by the…

A: Here, the given region is bounded above by the curve y=g(x)=4 and bounded below by the curve…

Q: r(t) = 2ti - 2tj + 시 6 t³k

A: Given :

Q: 6. Use Green's Theorem to find the counterclockwise circulation and the outward flux for the field F…

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Q: Solve: 2|z-21 +4>7 The answer has form: Ox B OA<x<B Where A- and B

A: We have to find the value of A and B

Q: More on Areas. Farmer Jones, and his wife, Dr. Jones, both mathematicians, decide to build a fence…

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Q: 1. Show that F is a conservative vector field and then find a function f such that F = Vf where F(x,…

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Q: Use the figure to find the exact values of sin(2u), cos(2u), and tan(2u). X sin(2u) = cos(2u) =…

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Q: Find the area of the region between the curves y = 12 - x² and y = x² – 6. Area between curves =

A: To find the area between the given curves

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: If f f(x) dx = 12, then ff(4x) dx is equal to If f f(x) dx = 12, then fx f(x²) dx is equal to

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Q: Find the limit. NOTE: Enter the answer using round brackets. t² +9 1 = lim t→+∞ (?, ?) 7t² + 8' 4t,

A: Given problem:-

Q: Suppose you deposit $1000 at 7% interest compounded continuously. Find the average value of your…

A: To find out the average value of account during first 4 years.

Q: and the magnitude of the given vector. (-4, 4, 7)

A:

Q: 4. Find the Taylor series for f(x) centered at the given value of a. [Assume that has a power series…

A: First we will find expansion using general formula and then put the value .

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: Find all solutions to the equation. sec²x + tan x = 1 Write your answer in radians in terms of , and…

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Q: The heights h, and h₂ (in feet) above ground of two people in different seats on a Ferris wheel can…

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Q: 4. A unit vector orthogonal to A and whose representations are parallel to the yz-plane.

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Q: Find the integral of the following equation integrate (cos x)/(1 - cos^2 x) dx

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Q: Find the Maclaurin series and corresponding interval of convergence of the following function. f(x)…

A: Let's find.

Q: A fungus starts off weighing 23.1 grams. Its mass increases by 1 percent every day, that is, each…

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Q: y"+4y'-45y 3 cos (6x) =

A:

Q: find the total differential dz. xety

A: dz=∂z∂xdx+∂z∂ydy ----&gt;1Consider z=xex+ythen∂z∂x=ex+y+xex+y∂z∂y=xex+y

Q: Find the maximum area of an isosceles triangle inscribed inside the ellipse x²y² 1, + = a² 62 with…

A: Given problem:- Find the maximum area of an isosceles triangle inscribed inside the ellipse x2/a2…

Q: 2. Evaluate the following (Express all answer in Rectangular Form): d. √9+ 2i e. 2¹ + ln(2 + i)

A:

Q: 4. sinx 1-sin² x dx

A: integration

Q: Prove the identity. (secx+1) (secx-1)=tan ²x Note that each Statement must be based on a Rule chosen…

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Q: Let f(x)=8+ √6x-3. Find f¹(z). f-¹(x) =

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Q: Let S be the solid obtained by rotating the region shown in the figure below about the y-axis. y…

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Q: 27 SECOND DERIVATIVES Find TUTORIAL 22 if y-In (x + 1). Answer 2-2x² 22-2

A: Note:-As per your mentioned request i am solving question 1 from the given figure.

Q: Use Green's Theorem to evaluate the line integral ſ (y + e√x) dx + (2x + cos y²) dy, where the given…

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Q: Find curl F and div F given F(x, y, z) = e* siny i+ esinzj+e-² sin x k

A: Given  Fx, y, z = e-x sin y i + e-y sin z j + e-z sin x k We have to find curl F and div F.

Q: Calculate S3, S4, and S5 and then find the sum for the telescoping series where Sk is the partial…

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Q: . DO NOT SIMPLIFY YOUR ANSWERS. - 1. log₂ 19²( √/2x² + y) + tan(x² − x²) = sin^¹(x² − 1) + ² Find d

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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: Evaluate the definite integral. NOTE: Enter the exact answer. |ti + t²j|| dt =

A: ||xi + yj || = √x^2. + y^2

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

A: As per Bartley guidelines we are supposed to answer only three subparts of one question per post.…

Q: x² 5x w Given that f(x) 3 a) find f'(x) b) find the equation of the tangent line x = 1. 1 12. Given…

A: Let's find.

Q: r(t) = cos(at)i ln(t)j + √t − 4k; to = 5 2 ms of i, j, and k. Domain is: (, ) NOTE: Enter r(5) ||…

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Q: Use Newton's Method to approximate the zero(s) of the function. Contine Rx)-x+2.7x² +3.55x-2.422…

A: answer is in next step

Q: Find the exact length of the curve. X √(y - 3), 16 ≤ y ≤ 25

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Q: 10 (1 - 6x)² convergence R Represent the function Co= C1 = C2 = C3 C4 = Find the radius of || as a…

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

A: Cos(c+d) = Cosc.Cosd - Sinc.Sind  Sin(c+d) = Sinc.Cosd - Cosc.Sind

Q: (D²+1)y= tan x

A:

Q: 2. Show that F is a conservative vector field and then use that fact to evaluate SF. dr along the…

A: We need to show F is conservative vector field.

Q: Match the vector field with its graph. F(x, y) = yi 址 四 場 x Q 6 電

A: F(x,y)=yi So at any point vector magnitude is same as y-cooridnate Also, if y is negative [below the…

Q: (1) What is the approximate volume of a thin cylindrical shell with height 2, radius 3, and…

A: Solution ) Volume of the cylinder    V = πx2h        x = radius         Differentiate with respect…