|r'(t) × r"(t)|| Use the formula k(t) to find k(t). ||r(t)||* r(t) = 11 cos(3t)i+ 11 sin(3t)j+ 7tk K(t)

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A: Equation of tangent line of a function f(x) at (a,b) is given by, y-b= f'(a)(x-a)

Q: ASK YOUR TEACHE Find sets of parametric equations and symmetric equations of the line that passes…

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Q: Which of the following is true for the series 3n? Σ 4n3 +9 n =0 Converges to 0 O Divergent O None…

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Q: decimal number o.11 11 Eaual ^ true O evror

A: This is a problem related to decimal points conversion into p/q form. Please follow the procedure…

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A: A vector v with given magnitude in the direction of u is given by v.uu.

Q: (a) u v (b) n.n (c) v||? (d) (u v)v (e) u (3v)

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Q: 10. On a typographic map, the contour lines show changes in elevation of the land. You and a friend…

A: a) From the figure I have an elevation of 200 ft and the elevation of my friend is = 800 ft. So the…

Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

A: The domain of the function is the set of all possible input values for which function is defined .

Q: Determine if the given sequence converges or diverges. If it converges, what is its limit? 5 + 3n3…

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Q: 5x 5y 7x²47 7x+7 • 0). Calculate div(F) and curl(F). (Use symbolic notation and fractions where…

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Q: The geometric series 4 5-2+ 5 16 + 25 8 32 125 625 is convergent. true false

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Q: 5x2 + x + 16 dx x3 + 4x 9)

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Q: Continuity: a. Determine the points of discontinuity and classify them. b. Give the domain and range…

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Q: Give the curve r = 3 cos 0 b) Find the points on the given curve r = 3 cos O where the tangent line…

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Q: Find the derivative of the function. 6x - 7x2 + 4 f(x • x³ - 3 f'(x)

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Q: Find the derivative of the function described. (Rx5) 3. f (x) = (1 +x + x² + x³ )'³

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Q: Solve the equation: Зx(ху — 2)dx + (х3 + 2у)dy %3D 0. O x³y – 3x² + y? = c O 3xy – 3x? + y² = c

A: Here is the solution

Q: (c) Determine whether the following function continuous at point (0, 0). Justify your answer. x²-xy…

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Q: Find the mass and center of mass of the lamina bounded by the graphs of the given equations with a…

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Q: Find the arc length of the parametric curve. x = e', y = et, z = v2t; 0<t < 8 L ||r'(t) × r"(t)||…

A: Given parametric curve x=et  , y=e-t  , z=2 t   ;  0≤t≤8

Q: Basic Derivatives: Find the derivative = (1 + vx* kx° V 8. f(x)=- 7x – 4x? x +2x y° – 5y³ + 2y 6.…

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Q: 1. Trace the curve whose equation is x* – x' y = -7x² + x+6 х* + 3х-10 Identify the following a.…

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Q: given magnitude and the same direction as u. Magnitude ||v||-5 Direction u- (-4, 6, 4) Submit Answer

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Q: (2x3 – xy? – 2y + 3)dx - (x²y + 2x)dy = 0

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Q: Find f'"'(x), the third derivative of f, and f (x), the fourth derivative of f. f(x) = 7x* + 2x³ +…

A: In the original solution it had been shown that:  f4x=ddxf'''x=ddx168x+12=1681+0=168

Q: Let f(x) = r³ – 3.r² + 4. Using the Mean Value Theorem, determine the value of c € (0,3) such that…

A: Given    f(x) = x3-3x2+41. Continuity:     we know that, every polynomial function is continous in…

Q: Find the area of the region between the graphs of f (x) = 3x3 – x² – 10x and g(x) = -x2 + 2.x, %3D -…

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Q: Consider the function f(z) =1-4x on the interval -4, 5]. Find the average or mean slope of the…

A: f(x)=1-4x2f(5)=1-4(25) =-99f(-4)=1-4(16)=-63The average or mean…

Q: Determine

A: We have to determine the given series is converges or diverges

Q: The base of a three-dimensional figure is bound by the circle x² + y? = 16. Vertical cross sections…

A: Given  x2+y2=16y2=16-x2y=16-x2

Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) = V…

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Q: Determine whether the following series converges or diverges. Σ 5n2 +5 n=1

A: We can solve the given problem as follows:

Q: 5. Find the derivative if yyx – 8 = xy + 2

A: yx-8=xy+2Differentiate w.r.t x

Q: ||r(t) × r"(t)|| Use the formula k(t) = to find k(t). r(t) = 8 cos(6t)i + 8 sin(6t)j+ 7tk K(t) =

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Q: A block of mass m = 2.00 kg is attached to a spring of force constant k = 410 N/m as shown in the…

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Q: The diagram at the right represents the height of a blimp flying over a football stadium. Find the…

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Q: B. NONHOMOGENEOUS EQUATIONS: UNDETERMINED COEFFICIENTS 2. (D2 + D – 2)y = 2x – 40cos2x 3. (D² + 1)y…

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Q: What is the area of the region bounded above by y = -x- + 8 and below by y = x? 54 $2 14 1 23 4 5 64…

A: This is a problem related to integration. Based on the formula of area bounded by given region we…

Q: If we apply Rolle's Theorem to the function f(x) = 2x – 12x – 3 on the interval [1, 5], how many…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Fill in the missing values to make the equations true. (a) log, 4 - log, 5 = log, %3D (b) log,+…

A: logarithm expressions are given,. we have to find the missing values

Q: The radius of the circle 2x? + 2y? – 4 = 0 is equal to 2 units. O TRUE O FALSE

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Q: The radical center does not existif the circles are concentric TRUE FALSE

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Q: Eliminate the constant 'a' from the equation. (x – a)² + y? = a² O (x? – 2y)dx + 2xydy = 0 (x² – y²…

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Q: Describe the graph of the equation. r = (8 - 3t) i - 14t j O It is a line in 2-space that goes…

A: Let's find.

Q: 3. Find the derivative of y = sin² 3x two different ways, a. Use the product rule. b. Use a power…

A: Here is the solution:

Q: dz of the following functions: Find dx 8 zx*+cos y? = sin(y °+ 22z)

A: Find your answer below

Q: Solve the following system of differential equations. dx —х — у, || dt dy Зх — у dt

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Q: Use the Mean Value Theorem in applications Question If a rock is dropped from a height of 37 ft.,…

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Q: Which of the following is a particular solution to the differential equation dx when x = e5 and y =…

A: We are asked to find the particular solution of the differential equation

Q: Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy if…

A: Here we have to determine whether the given function is continuous or not.