Define two vector functions r(t) = 4 sin(t)i + 3 cos(t)j + t²k ū(t) = 3 sin(t)i + 4 cos(t)j + t³k Compute r(t) u(t) : =

Q: Transform the following equation of ellipse in standard for 7x²-10v² 56x +100y +278=0

A: 7x2-10y2-56x+100y+278=0 We have to convert into standard form. Lets first make a perfect square in x…

Q: Find the derivative of the function using the chain rule (not the "u" version)   *please use…

A: Disclaimer: According to our guidelines we cannot provide you handwritten solutions at the moment .…

Q: Evaluate the derivative of the function at the given point. Use a graphing utility to verify your…

A: To find derivative of function at given point

Q: how to apply the chain rule the following equation Y=sin 5x/2

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Q: Find an equation of the plane that passes through (8, -2, -3) and is perpendicular to the vector (1,…

A: Topic = Coordinate Geometry

Q: Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit…

A: Rate of change of a functio y=f(x) is given by y'=dydx=df(x)dx

Q: Y=x5e-3 ln x

A: Topic- derivative of a function . we are given , y=x5e-3ln x and we know that Product rule…

Q: For f(x) = 10/x and g(x) = 10/x, find the following function (fog)(x) U I=

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Q: If y = (Inx)² + 15, find dy dx

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Q: Find the coordinates of points where the graph of f(x) = -x³ + 6x2 - 9x + 19 has horizontal…

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Q: Use the four-step process to find r'(x) and then find r'(1), r'(2), and r'(3). r(x) = 3+3x² r'(x) =…

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Q: Find the area of the triangle PQR

A: As we know that; If the vertices of the triangle△PQR are given, then the expression for the area of…

Q: 3. 72 – 4 – 3 lim 1 32 – 4 + 1

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Q: Find the speed at the given value of t: r(t) = (et-5, 12,5t-¹), t = 5 v(5) =

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Q: A car company can sell x cars at a price of p(x) = -0.01x + 800 dollars per car. The cost of…

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Q: Answer the following questions: 1- Find the domain of f(x) = x²-4 x-2

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Q: If the nth derivative of y is denoted as y() and y = -sin x, then y(23) is the same as

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Q: Given 1 surface area, A: = πγ2 + πrl. If value of r changes from 6m to 5.8m and value of I changes…

A: Given surface area, A= πr2+πrl  Taking derivatives each sides we get, dA=2πrdr+πldr+πrdl...(i)

Q: Find Əx Select one: O a. O b. if Sxy= 3x +y10 O C 3-8y 10y⁹ - 8x 8x-3 10x 8y-9x 10

A: The given equation is; 8xy=3x+y10.

Q: Evaluate the integral. π/4 0 (sect tanti+t sin 2t j + sin³ t cos t k) dt

A: The answer is given below:

Q: Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation for…

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Q: An airplane flies at an altitude of y = 4 miles toward a point directly over an observer (see…

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Q: Find the general solution of the differential equation Write your solution in the form F(x, y) = C,…

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Q: x = 22t, y = 3t, z = 1+ t; x + 2y - z = 7 -

A: Topic:- algebra

Q: For f(x)=5x-1 and g(x)=x+1/5 find the following function (fog)(x)

A: given that f(x)=5x-1 and g(x)=x+15 find (fog)(x)?

Q: Determine 1) a₁ = -3, r=4 if each geometric series converges or dive 3) a₁ = 5.5, r=0.5 5) 81…

A: Solution

Q: Find an expression for the inverse of f(x) = e³x+1. f-¹(x) = 4

A: Topic- functions and inverse functions We are given, f(x)=e3x+1 we know that ln(ex)=x

Q: What are the three ways a function is not different at a point x=a? ( sketch the graph for wash…

A: Guven question:- What are the three ways a function is not different at a point x=a? ( sketch the…

Q: The total sales of a company (in millions of dollars) t months from now are given by S(t) = 0.04t³…

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Q: Consider the following. 1 - 2x² x42x² + 3 Let u(x) = 1 - 2x² and v(x) = x² − 2x² + 3. Find each…

A: We need to find derivative.

Q: Find the derivative of the function. 3 2 + X g(x): = X + 93√x

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Q: 6. 3.x lim x-1 x² + 2x + 1

A: given that limx→-13xx2+2x+1

Q: Find the domain of the functions below. f(x) = √x + √5 − x h(x) = (x − 4)−1/4 Enter your answers…

A: Formula: Domain of a square root function: f(x)= √y  can be find by y≥0

Q: Find the derivative of the function using the chain rule  *please use handwriting not typing. i…

A: Let's find differentiation of given function.

Q: U = {x: x is first ten positive integers} A = (1, 2, 5, 6, 9, 10} B = (2, 4, 6, 8, 10} C=(3, 4, 7,…

A: Given: U=x: x is first ten positive integersA=1, 2, 5, 6, 9, 10B=2, 4, 6, 8, 10C=3, 4, 7, 8To Find:…

Q: If an object moves along a line so that it is at y = f(x) = 5x² - 2x at time x (in seconds), find…

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Q: Find the equation of the plane containing the point (-4, 6, 1) and parallel to the plane 6x7y2z = 0.

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Q: Find f + g, f-9, fg, and f/g and their domains. f(x)=√√16x², g(x) = √√x + 2 Find (f + g)(x). X Find…

A: Find the function and their domain

Q: Sketch the interval (a,b) on the x-axis with the point c inside. Then find the largest value of 8>0…

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Q: A bag contains 2 gold marbles, 7 silver marbles, and 25 black marbles. Someone offers to play this…

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Q: Solve the Initial Value Problem F(x, y) = 7 lny- y' Express your answer in the form F(x, y) = = 33 =…

A: This question can be solved using the concept of homogeneous differential equation.

Q: Use implicit differentiation to find an equation of the tangent line to the curve -4x² + 1xy - 3y³ =…

A: This question can be solved using the concept of tangent and normals.

Q: (Technology Permitted) The position of a particle moving on a horizontal line is given by…

A: We need to choose correct option.

Q: y = f(x) N.K. X -1- (a) lim [f(x) + g(x)] (b) lim [f(x) = g(x)] - (c) lim [f(x)g(x)] -1 y 1 y = g(x)

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Q: Consider the following initial value problem: (t²- 20t+51). =y with y(10) = 1. dy dt A. Solve the…

A: We know, ∫ dx/x = ln|x| A. Given differential equation, (t²-20t+51)dy/dt =y  So, dy/y =…

Q: For what values of m and n will µ = x^ym be an integrating factor for the differential equation (-4y…

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Q: Given f(x)=8+3/x and g(x)=3/x find the function f-g Also find the domain for the function

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Q: Verify that the given point is on the curve. Find the lines that are a. tangent and b. normal to the…

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Q: ← Find the following limit. lim X-0.2 lim X-0.2 x+5 √x+1 x+5 √x+1 ... کا و ایران کانوں

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Q: Sketch a graph of ƒ(x) = = 8 7 6 Clear All Draw: 5432 5 4- 7 -8-7 -6 -5 -4 -3 -2 -1 1 -2 234 -5 67 7…

A: given f(x)=2x+611.5x-5if     x≤-1if  -1<x≤4if x>4