Find the Maclaurin series of $1.² n=0 sin(t) to -dt.

Q: Find the length of the following two-dimensional curve. r(t) = (5 cos ³t, 5 sin³t), for Osts sts R|N…

A: To find the length of the following two-dimensional curve.

Q: Given that y = (2³ – 3) (z + 7). Find the derivative using the product rule and simplify your…

A: If we have a function , where u and v are the functions of x  . Then, by the use of the product…

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Q: Determine the following limits: (a) 42³-19z²+12z lim x 0 7x³-23x2-20x Number (b) 423-192²+12x lim x…

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Q: Consider the helix r(t) = (cos(3t), sin (3t), - 2t). Compute, at t = : A. The unit tangent vector T…

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Q: derivative y = 3 2(4x-1)

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Q: Determine whether the equation is exact. If it is, then solve it. e'(7y - 4t)dt +(3+7e¹) dy = 0 A.…

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Q: What is the moving point's acceleration vector when t = (0,25) (0,10) (0, 0) (5,0) 0?

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Q: Step 1 • 1² -√² f(x) dx = 3 Note that Step 2 To evaluate Therefore, fax) f(x) dx, substitute frox…

A: Find integration of f(x), x from  3 to 6.

Q: Let f(x)= 2x1 3x + 2 a. Find the domain of the function. b. Find the y-intercepts, if any. c. Find…

A: The given function .The aim is to find the vertical and horizontal asymptotes and sketch the graph…

Q: Differentiate. h(w) (w³ + 4wª) (w 4 - w-6) = -4. −6) (5w4 + 16m³) + (w³ + 4w4 ) ( −4w−4 – 6w¯ - W…

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Q: et f(x) x8(x-4)³ (x²+3)8 Use logarithmic differentiation to determine the derivative. ƒ'(x) =

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Q: B 2. Find fæ, fy, fay, fax and fyy for the functions (i) f(x, y) = x²y³ + x³y5; (ii) f(x, y) = x²…

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Q: Find the directions in which the function increases and decreases most rapidly at Po. Then find the…

A: We solve the given problem by using the concept of the gradient of a function.

Q: Evaluate the following limit by simplifying the expression (first answer box) and then evaluating…

A: given limit

Q: The volume of a cube is decreasing at a constant rate of 2371 cubic centimeters per minute. At the…

A: The volume of a cube is decreasing at a constant rate of 2371 cubic centimeters per minute. At the…

Q: Use a graphing utility to graph the quadratic function. f(x) = x² - 4x -10 O -10 -5 (x, f(x)) = S…

A: x intercept is the point where the curve crosses the X axis.

Q: Let f(x, y) = y²x − yx² + xy. (a) Show that the critical points (x, y) satisfy the equations y(y -…

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Q: Find the limit. Use l'Hopital's Rule where appropriate. If there is a simpler method, consider using…

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Q: Suppose we know that y = 2z4+3 z³ - 16 and x = 2 t² - 3 t-4. Compute the following quantities: da…

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Q: Use the method for solving equations of the form following differential equation. dy dx 19x + y - 19…

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Q: A particle is moving along the x-axis. The position of the particle at time t is given by x(t) = t³…

A: A particle is moving along the x-axis. The position of the particle at time tis given byTo find the…

Q: O The following differential equation is a Euler equation. Find the general solution of 2x²y" + 5xy'…

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Q: The volume of a right circular cone of radius & and height y is given by V = the volume of the cone…

A: Given:

Q: Find a vector orthogonal to both ⟨1,−4,0⟩ and to ⟨0,−4,2⟩ of the form ⟨1,_____ ,_____ ⟩ 9. Let…

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Q: 100 100 100 t Σ ai = 6 and Σ b; = −4. Then compute Σ (2a; + 5b; – 3i + 1). i=1 i=1 i=1

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Q: Use spherical coordinates to find the volume of the smaller wedge cut from a sphere of radius 9 by…

A: To findThe volume of the smaller wedge cut from a sphere of radius 9 by two planes that intersect…

Q: 1 (a) f(x) =====₁ x+1 (b) f(x) = √√√√x − 4 (c) f(x) = 1 x-3 (d) f(x) = 2x² + 3x +9

A: To find the domain of each of the following functions.

Q: Let f (x) f'(x) = = sin−¹(x²) – tan−¹(6x + 1). Find the derivative of f. 6

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Q: Use the chain rule to find the derivative of f(x)=5(-527-82³) ¹4 Leave your answer in factored form.…

A: Consider the function

Q: Əw ər Find when r = 5 and s= -5 if w= (x+y+z)²₁ x=r-s, y = cos (r+s), z = sin (r + s). Əw ər = |r =…

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Q: Find the value of a for which v= 8 a -4 -12 is in the set 4 0 -4 -1 0 {6E9 2 -3 5 -3 -4 2 H = Span

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Q: Given h(x) Degree of h = 4 3x + 6x + 24x answer the following questions: The leading coefficient of…

A: The x intercept of a function is the point where the graph crosses the x axis.The yintercept of a…

Q: B 4. z (x, y) is defined implicitly by the relation z²x - 2yz +xy² = 4. Find za, zy and Zaz in terms…

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Q: The view V, or distance in miles, that one can see to the horizon from a height h, in feet, is given…

A: The view V, or distance in miles, that one can see to the horizon from a height h, in feet, is given…

Q: 2. An object weighing 27 pounds is thrown downward with a speed of 2 ft/sec and falls to the ground…

A: weigh of the object = 27 poundsdownward speed = 2ft/sWind resistance = 3% of the square of the…

Q: (a) (c)= dx (c) & √(x²). (e) d [ƒ(g(x))]= (g) (sin x)= dx (i) --(tan x) = dx d (k) (sec x) = dx (m)…

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Q: Sketch the region bounded by the curves y = 3 − x 2 and the line y = 2x, and find the area of the…

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Q: Find the Maclaurin series of n=0 sin(x) 26

A: The given function .The aim is to find the Maclaurin series of the function.

Q: Given h(w) Degree of h = 8 -0.016(4-2w)(-10-3w) (2w+7) answer the following questions: . The leading…

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Q: Find the volume of the solid bounded by the graphs of x² + y² = 4, z = 4x + 5y, and the coordinate…

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Q: In(t+7)=-1 in exponential form

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Q: Write the standard form of the quadratic function whose graph is a parabola with the given vertex…

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Q: Use the Second Fundamental Theorem of Calculus to find F'(x). • L₁ VE 4 + 4 dt Vt Step 1 F(x) = Note…

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Q: B. Given the function defined by f(x)= continuous at: i. x=1 ii. x=3 (3x-2 5x-1 2 2x-3 x23 1<x<3,…

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Q: 4) Consider the closed curve in the xy-plane given by : 6xy = 2+y³ dy a) Find dx b) Find the…

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Q: Use the unique factorization theorem to write the following integers in standard factored form. a.…

A: The given numbers,(a) (b) (c) The aim is to write the numbers in standard form by using the unique…

Q: Consider the function y = 2e4. Which of the following statements is true for y? O y'=y Oy = /v O…

A: given,

Q: Write the following in standard form and explain your work. 9y² + 11x² + 132x +297 = 0

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