Problem 2: Let v=⟨3,4,5⟩.  Find a unit vector in the same direction as ?. ⟨_____,_____ ,____ ⟩

Q: : Consider again the space curve c(t) = (1,9 cos t, 9 sin t). Compute the associated unit normal…

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Q: Given the function f"(x) = x²(x − 3)²(x - 5)³, what conclusion can be drawn directly from the sign…

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Q: Let R be the region bounded by y=x², x= 1, and y=0. Use the shell method to find the volume of the…

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Q: 2. Consider the region (shown below) in the first quadrant bounded by y = x(x - 1)2, y = 0, between…

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Q: /3 3

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Q: Net Signed Area Next question If the function f is continuous on [a, b], then the net signed area A…

A: Given that, the function         We need to use the given definition to find the area of the…

Q: As blood moves through a vein or an artery, its velocity v is greatest along the central axis and…

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Q: An arrow is shot into the air and its height in feet after t seconds is given by the function f(1) =…

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Q: [(1-sin' 3t)-cos3t dt

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Q: 8. Find the indefinite integral: x*e*2* dx (Use the "shortcut", Parts "Tabular Method", aka "Parts…

A: The given integral

Q: Question 1 Sketch the graph of f(x); do not forget to keep some sense of a scale and to identify any…

A: The given function is

Q: An oil storage tank ruptures at time t= 0 and oil leaks from the tank at a rate of r(t)= 80e-0.01t…

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Q: Write the first five terms of the sequence of partial sums. 1 + = + = 1 + 1 / / / + Select one: O a.…

A: we are given the series we are to find the first five terms of the squence of partial sums of the…

Q: 2. A spring has a natural length of 10 cm. It takes 1 J to stretch the spring from 10 cm to 15 cm.…

A: Given:Length of spring - 10cmWork done to stretch the spring to 15cm - 1J

Q: "W Σ M=1 8 (n+5)(n+7)

A: S=∑n=1∞8(n+5)(n+7)

Q: Assume that -- 10. 10, and -1. What is the value of Sü(7ü-50)?

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Q: Determine whether the equation is exact. If it is, then solve it. (3x²y +8) dx + (x³ -8) dy = 0 For…

A: Given differential Equation is as follows

Q: The graph of a function f is given. Use the graph to estimate the following. y 2 N X

A: Given graph of function

Q: Solve the following differential equation dy dx 1 1+x8 = 4. 3y X such that y(1) = 0.

A: Given Linear differential Equation is given as follows standard form of linear equation

Q: Find a possible equation for the linear function g(x, y) shown in the graph below: g(x, y) = -3 -8.…

A: Given that, the contour diagrams.We need to find the equation of the linear function .One of the…

Q: Use the graph of f(x) to answer the following questions. (a) (b) lim 8118 f(x) = lim x-1+ f(x) = $

A: The graph of the function  is given below.:To find the following: Note: Since the student has…

Q: e²x e³ +e²_2dx. S

A: To solve the following integral.

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 50x + 0.8x² -…

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Q: 5) Which of the following functions is differentiable for all real numbers a) y = |x²-91 b) y = √10x…

A: The given functions

Q: 3. Determine whether the given vectors are orthogonal, parallel, or neither. (a) a =, 6= (b) a =, 6=…

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Q: Use an appropriate trigonometric identity and substitution to evaluate the integral: tan’ r sec rdr

A: Given Indefinite integral as follows As we know that

Q: Find the volume of the solid formed by rotating the region enclosed by y = e +4, y = 0, x = 0, z =…

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Q: 7. Given min(x, y)= y, x>y x, y>x Find d d dy dx min(x,y).

A: Given function is:

Q: 4. Given to the right is the graph of the derivative of a function,f x ( ). Iff (0) 9 , what is…

A: The objective of this question is to find the value of the function f at x=2, given the graph of its…

Q: Use the general slicing method to find the volume of the following solid. The solid whose base is…

A: Given that a solid whose base is a triangle with vertices  and whose cross sections perpendicular to…

Q: 4) Calculate lim (√t-3, V-2, tan t-4 t-4 (-)). HINT: On the second component, you can factor t - 4…

A: To find:-

Q: Consider again the space curve c(t) = (t, 5 cos t, 5 sın t). Compute the associated unit normal…

A: c(t)=<t,5cost,5sint>

Q: er h(x) = 4x³ + 7x² - x³ + 7x

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Q: (3) A 신

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Q: Determine whether the following series converges or diverges. If it converges, find the sum. (2² 1…

A: Geometric series

Q: 5. The shape shown below is made up of 8 equilateral triangles. Let TQ = u and SQ = v. T ū Write an…

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Q: st be flawed. b) Some numbers have two different decimal representations. Specifically, any decimal…

A: he phenomenon you're describing is related to the concept of repeating decimals and their equivalent…

Q: During the time interval 0 ≤ t ≤9, the rate of change of the population of deer in a forest, in deer…

A: The statement V′(7)=125 represents the derivative of the population function V(t) at t=7, which is…

Q: 2: Consider a particle that travels along the path given by c(t) = (2 sin(6t), 2 cos(6t), 216 + 1)…

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Q: Suppose that demand for local cable TV service is given by p=114 -0.4x where p is the monthly price…

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Q: Solve the initial value problem. 2 4x -x-3 XN = dx (x + 1)(y + 1)' 11 y(1)=2

A: given differential equation

Q: Which of the following is an Initial Value Problem (IVP)? (i) y' + 13y = 0, y(6) = 0, y(13) = −7…

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Q: Assignment 4 Problem 3: Let a=⟨1,4⟩ and b=⟨5,−4⟩. Show that there are scalars s and t so that…

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Q: determine the absolute extrema of the given function on the specified interval. g(z) = z²e¹-² on 15…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: Evaluate 2 Cot 2 / dx ct x 3 k 742

A: The given integral

Q: Suppose that the cost function for a commodity is C(x) = 70 + x² dollars. (a) Find the marginal cost…

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Q: Find all values of a where the function f(x) = = xe -52+4 has a relative extrema.

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Q: What is the distance from the point P=(2, -1, 4) to the plane 3x+5y-2z =20

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Q: Which of the following is true in explaining the convergence of fixed-point iteration g (x) = x + 2?…

A: Given that, the function is   ,we need to find the convergence condition of fixed point iteration…

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

A: We need to find the volume of the solid region about y-axis.