Determine the interval(s) on which the vector-valued function is continuous. (Enter your answer using interval notation.) r(t) = Vti + Vt - 1k

Q: Use a Maclaurin series in the table below to obtain the Maclaurin series for the given function,…

A: The objective is to obtain the maclaurin series of the given function.

Q: frite the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.…

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Q: 4. S V4x –1 dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: one-to-one function is given. Write an equation for the inverse function. x-3 t(x) = x+7 () = D %3D

A: Given query is to find the inverse function.

Q: TOPIC 1: Illustration of an Antiderivative of a function. (p.225) Written Works Determine the…

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Q: Solve the equation. Write the solution set with the exact solutions. log10 (7-m) + log10(-m-2) =1 If…

A: logb(m)+logb(n) = logb(mn) logby =x is equivalent to bx =y.

Q: 2 -4 8. 0 and P=0 1 -4 Let A 0 -1 00 1 Given that P diagonalizes A, then compute each of the…

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Q: dx Evaluate: xV x2 + 4 x² + 4 – 4 + C x2 + 4 + 4 - A) 4 x² + 4 – 2 +C x² + 4 +2 Vx² +4-2 + C Vx² + 4…

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Q: fx) dx = -5x* + 3x² + 6x + C

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Q: Question Use the First Derivative Test to find the location of all local extrema for the function…

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Q: Use the indicated change of variables to evaluate the double integral. (Round your answer to two…

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Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A: We have to find volume of solid formed by rotating the given equations about X - axis.

Q: 2. Let f(x) be a function of period 27 such that f(æ): over the interval 0 < x < 2x. a) Sketch a…

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Q: If f(x) = kx, determine the value of k that makes f(x) a probability density function on 0<xs4.

A: Given,           fx=kx2To find : Determine tha value of k that makes fx a probability density…

Q: Question Evaluate the following limit using L'Hospital's rule. lim + sin (6x) Provide your answer…

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Q: Consider the following. u = (-2, 5, 4) v = (0, 1, 7) %3D Find u x v. Determine if u x v is…

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Q: 1. S v2x – x² dx 1+x2 2. S* dx 1+x3 3. SV1+ v1+x dx 4. Set up only the integral(s) that will compute…

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Q: 6. DETAILS LARCALC11 12.R.020. 0/1 Submissions Used Find r'(t), r"(t), and r'(t) · r"(t). r(t) = 8…

A: A detailed solution is given below

Q: Find the absolute maximum and absolute minimum of the function f(x) = -2 sin² (x) over the interval…

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Q: Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y'…

A: Let's find.

Q: Find the area of the triangle with vertices P(1,5, –4), Q(0,0, 0) and R(4, 5, 1). NOTE: Enter the…

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Q: 2. Set up the integral to calculate the area between the curves (f(x)-g(x)) dx f(x) = x²+2x+1 8(x) =…

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Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: 1. When finding the anti-derivative of a function, what is the rationale behind hav- ing a +C ?

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Q: ACTIVITY 2: Find the derivative and simplify the result, if possible y = x2 + n² +x" y = x2 sec x y…

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Q: The interesting relation is x^2+y^2 = 13. I have drawn it and completed part 1. Part 2 is determine.…

A: Topic:- geometry

Q: PART C dy 12. Show that dx 2 for the relation %3D V%3D10, x, y X. # 0. y

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Q: Question The statement below is of the form ren de = F6x) + C. Verify whether the following…

A: Note that: ∫-4x55-5cos(x)dx=-45∫x5dx-5∫cos(x) dx=-45x66-5sin(x)+C=-215x6-5sin(x)+C

Q: please

A: We have to choose the correct option from the given options according to the given information

Q: Use the method of Laplace transforms to solve the given initial value problem. Here, D[x] and D[y]…

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Q: Find the rate of change of the function at a given value. 1. f(x) = 2x – 3, at x = 5 2. f(x) = 2x² ,…

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Q: Find a parameterization for the curve shown in the figure below. 1.0 F1 -1 F(t) where VI VI

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Q: 2. Locate the centroid (x, y)of the following areas: a) y3D Vx/2 + 2r/3 %3D I 2 ft

A: Given:    Centroid of the colored figure x,yWhere,x =MyM      &amp;       y =MxMMy = ∫02xfx-yxdx…

Q: The angle of elongation between Venus and the Sun is 26". Given that Venus is 67.2 million miles…

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Q: Find the value for k so that the function will be continuous at x = 3. - 10x? – 10x + 120 - 1 if x <…

A: The given function,  f(x)=-10x2-10x+120x-3-1if x&lt;3-7x2-70x-175+kif x≥3

Q: Equation is x^2+y^2 = 13, point (2,-3). Find the equation of the tangent OR normal at that point.

A: Given query is to find the equation of the tangent.

Q: Question 5 Find all the first sder partial derivatives for the following function. f(x, y) = x(x, y)…

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Q: Question The graph of f(x) is given below. On what interval(s) is the value of the derivative f'(x)…

A: Here we have to find the interval over which derivative of f(x) is negative.

Q: Find the derivative of the function. F(x) = dt

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Q: Question Evaluate the following limit using L'Hospital's rule. 10 lim 5* ( 3x2 24x +45 3x - 15…

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Q: 4. In the differential equation (6r-3y+2)\dr-(2x-y-)dy=0, we let the substitution =xp

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Q: For the functionf(x) given below, evaluate lim f(x) and lim f(x). f(x) = -5x + /25.x² – 3x Provide…

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Q: Test the series for convergence or divergence. Justify your answer. Σ *-3

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Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

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Q: Below is a sketch of the graph of J.

A: we say at x=a limit exist if the both right and left side limit exits and equal at x=a

Q: Find the gradient of the function at the given point. w = x tan(y + z), (3,9,-5) Vw(3, 9, –5) =

A: For a given vector fx, y, z the gradient vector denoted by ∇f is ∂ ∂ xf∂ ∂ yf∂ ∂ zf So, ∇w=∂ ∂…

Q: Find the area of the region enclosed by y = 4x and z = 6 – y. %3D %D 4 +2 Use horizontal strips to…

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Q: Decide whether the function defined as follows is a probability density function on the indicated…

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Q: S sin x (1+ cos x) ecos *dx 2. S csc ³ () do 1.

A: 1) Given:       ∫sinx1+cosxecosx dx Integrate by parts:         ∫fg′=fg-∫f′g here  f=1+cosx→f'=-sinx…

Q: pind projaB iF A > {l,0,27 B: <6,-2 ,3

A: A=&lt;1,0,2&gt;B=&lt;4,-2,3&gt;projAB=A.BA2.A