Find the unit tangent vector to the curve defined by r(t) = = 5t, 3t, √64-t²) at t = -1. Ť(−1) =

Q: Find the area of the region under the graph of f on [a, b]. f(x) = e-x/2; [-1, 6]

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Q: Find the domain of the vector functions, ?(?)�(�), listed below. using interval notation. ) ?(?)=⟨…

A: To find the domain of the vector function r(t)=⟨t−3,t2−4​1​,t1/3⟩, we need to consider the values of…

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Q: 1) Simplify the following: (Round to the nearest cent if money is involved) a) (2+3× 2)² - 4(5² -…

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Q: 7. Find the total mass of a circular plate of radius 20 cm whose radial mass density function is…

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Q: A sample data set has a mean of 72 and a standard deviation of 12. Determine whether each of the…

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Q: Find the derivative of the function. 3 f(x)=√x - ³√x

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Q: 83. T Bank account A $200 investment in a savings account grows according 200e0.0398t, for t≥ 0,…

A: Given function: , where is measured in years., initial balancea. To find the balance of the account…

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Q: 27. Determine the distance between the lines ở = (0, 1, −1) + s(3, 0, 1), seR with ở = (0, 0, 1) +…

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Q: Analyze the function below. Which of the following is/are true? 8 f (x²) 184²8 x+1 as x → −1+, f (x)…

A: Given: To Find: To determine the true statements.

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Q: Use the graph of f(x) below to find the following derivatives. Write DNE if the derivative does not…

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Q: Each derivative represents the first li Please state this original function, f(x f'(x) = lim h→0…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Fill in the blanks using the two graphs below. y = f(x) -10- -2 -3 -4 -10 f(6) y = g(x) *Be sure you…

A: We have to fill the blanks using the given two graphs.

Q: please asnwer all the questions please

A: Since you have asked multiple questions in a single request. As per guideline I will be answering…

Q: Find an equation of the tangent line to the graph of the equation at the given point. x² + x arctan…

A: The point on the curve through which tangent passes is, .The slope of the tangent is given by, The…

Q: Solve the initial value problem fort> -1 with y(0) = 3. y = dy dt 9(t+1)- - 7y= 14t,

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Q: Write the equation of the vertical line at which the graph is discontinuous. Then, write what y…

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Q: 2) Given the function f defined by f(x) = 7√9x²-1 a) Describe the symmetry of the graph off. Justify…

A: Explaination of the ans is as follows

Q: If f(x) = 3 sin x + 7 cos x, then ƒ'(x) = f(3) =

A: The given function

Q: if f'(x) = 5 - (8/x^2) , x≠0, find the value of f(4) given that 2f(1) = 4 + f(2)

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Q: SOLVE: Y" - Sy=0 -

A: given differential equation

Q: Given the function below, find the average rate of change on the interval [1,4]. -10- V -5 0

A: given graph of the parabolic function. To find : average rate of change of function on interval

Q: Find the constants a, such that the function g(x) continuous at a O O O a = Oa= 4 In 9 9 In 4 In 4 9…

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Q: The dimensions of a triangle are shown. cm 8 cm What is the area of the triangle? Use the number pad…

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Q: Solve for 0≤x≤ 10 3xln(sinx) + (sinx)x=4

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Q: Find all zeros, noting multiplicities and behavior at the zeros, of the following functions:

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Q: Find u v, uu, ||u||2, (u v)v, and u. (2v). . u = 5i + j - 9k, v=i4j + 5k (a) (b) u. V u u (c) ||u||²

A: According to Bartleby's guide line we only do first three parts of multi-part questions.Given,

Q: 45-60. Areas of regions Find the area of the following regions. 45. The region outside the circle r…

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Q: Set up and solve a first order IVP to solve the mixture problem. A tank is filled with 100 gallons…

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Q: The Ninth Gate You arrive at the final gate, which leads into a building-like structure. You hope…

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Q: b) The cross-section of the pelvic fin of this fish is modelled by the curve y=-2¹ +162³-24z²…

A: given cross section of the pelvic fin is

Q: How. 2 Evaluate the following cartesian integrals changing them into equivalent Polar integrals:…

A: The given integral is:The aim of the problem is to evaluate the given cartesian integral by changing…

Q: a. Find the solution to the initial value problem lim y(t) = t-30 y'e +3 y b. Discuss the behavior…

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Q: Without a calculator, identify the given key features of the polynomial and sketch a possible graph.…

A: The given polynomial equation is

Q: 28. Determine the point of intersection between the following pair of lines r = (5, 1, 7) +…

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Q: 2++ 32 N Graph of g The graph of the polynomial function g is shown. The function f is defined for…

A: In this question, we will find the local minima and maxima.

Q: 26. Find a vector perpendicular to both a = [1, 2, 3] and 5 = [3, 2, -1].

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Q: Find 7'(t), given r(t) = = 7' (t) = = (= 7t² -2t 3 -2t3 +5' 2t2 +6' -2t - 1

A: Given

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Q: Which of the following is an accurate conclusion that can be made using the existence and uniqueness…

A: In this question, we will find the initial value problem solution.

Q: Find the limit, if it exists, or type N if it does not exist. e√1x²+4y² lim (x,y)→(-4,1) e^8

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Q: (Text Suppose y = f(x) graphed in the figure below represents the cost of manufacturing x kilograms…

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Q: 2. A function y = f(x) passes through the origin. If the second derivative y" = -sin (2x), determine…

A: A function  passes through the origin. If the second derivative is given by , then to determine the…

Q: et f be the function defined by f(x) 0 x+7 Choose the correct answer below. Does not exist. . If f…

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Q: 2.) Evaluate the function for the given value of the independent variable. Simplify your answer if…

A: Note: As per our guidelines, we can solve first question. But I solved first two as your first two…