If r(t) 0, show that r(t) = r(t) · r'(t). ‡

Q: Find dy dx dx for y = √√√x(7x + 4).

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Q: 5) f(x)= x² + 3x 2x² - 4x

A: The given function isf(x)=(x2+3x)/(2x2-4x)According to  the Bartley guidelines we solve only one…

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Q: #3: Calculate the curvature x(t) for the space curve c(t) = (t, 7 cost, 7 sin t).

A: c(t)=(t, 7cost, 7sint)

Q: Match the sequence with its graph. 11 1" Select one:

A:

Q: Given the following radical function: P(t)=3√3t+9-7 State the Domain of P(t) in interval notation in…

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Q: Find dx² y = -5x⁹ +1 d²y dx² 11

A: The given function equtaion is

Q: 1 3 - -- () ---- () 5 V2 = 10 3 12 4. Let VI: a) For what values of his v3 in Span {V₁, V2} ? b) For…

A: The given vectors,.The objective is to find the values of  for which the vector  is in the  and  are…

Q: 5: Compute the associated binormal vector B(t) for the same space curve c(t) = (t, 7 cost, 7 sin t).…

A: We need to find Binomial vector B(t).

Q: Find dy du du dx dy dx y = 6u² + 3 and _u = x² + 3 I and when y and u are defined as follows.

A: given

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: "W Σ M=1 8 (n+5)(n+7)

A: S=∑n=1∞8(n+5)(n+7)

Q: 2. Find the exact angle between vectors a = 3 î - j - 2k – 18 10 b = v – w, wherev = 2î + ĵ + 4kandŵ…

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Q: The solution to y' = 4y - 8 with y(0) = 5 is A. y = 5e¹x C. y = 3e¹x + 2 B. y = 8ex-3 D. y = 4e* +1

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Q: r4 1 X 1+x² - dx

A: Consider the integral

Q: A Ferris wheel is 40 meters in diameter and boarded from a platform that is 4 meters above the…

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Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

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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: Use the shell method to find the volume of the solid formed when a hole of radius 1 is drilled…

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Q: Evaluate the function at the indicated values. (If an answer is undefined, enter UNDEFINED.) k(x) =…

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Q: 6 y = f(x) 5 4 E 3 2 1 0 y f(1) = 1 1 lim f(x) = I-4 I lim f(x) = z→9+ lim_ f(x) #45 = 2 3 Enter…

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Q: Evaluate the piecewise defined function at the indicated values. f(-8)= f(-3) = f(2)= f(3) = f(6) =…

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Q: Given that f is continuous on [0, π] and 6 TC [² x sin(x) 1 + cos²(x) πT dx xf(sin(x)) dx = π 2 T S…

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Q: Find the most general antiderivative of the function. (a) f(x) = x³ - 5x² + 3x -4 (b) f(x) = cosx +…

A: Note:-Since you asked multiple sub parts , according to our policy we can answer only first the…

Q: -8 Consider this function. 8 Here is one of the cards from earlier. As it turns out, this was one of…

A: given a function to find the derivative

Q: Using the definition of continuity, show that the following function is continuous q(2) = ² at zo €…

A: The function is given byTo Show: The function is continuous at .

Q: Use partial fraction decomposition to evaluate the integral: √2²+ X x²+x-6

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Q: lim x-0 3Cosx-3-Sin3x 4x

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Use Shell Method to find the volumes of the solids generated by revolving the shaded region about…

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Q: (sec² (sec²(t) i + t(t² + 1)³ j + t7 In(t) k) dt

A: Vector integration

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y - 4xyz + 7yz²…

A: The given function is f(x, y, z) = 3x2y − 4xyz + 7yz2

Q: The position of an object at time t is given by the parametric equations [x = 4t2 + 4t y = 2t² + 2…

A: The objective of this question is to find the horizontal velocity, vertical velocity, and the speed…

Q: Find all intervals on which the function ƒ(x) : = e 2x -3x+3 is decreasing.

A: given function

Q: Please explain each step and graph the following: Graph the equation y= -4x2

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Q: Determine if each function below is invertible : (Include all steps) a) y=2x^2-1 b) y=(6x-1)/(1+3x)…

A: Note:-Since you asked multiple subparts,according to our policy we can solve only first three sub…

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: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing (in…

A: The radius of a sphere is increasing at a rate of 4 mm/s.To determine the rate at which the volume…

Q: Given that 8 [f(u) du = K. Find 2 [² x ². 2 x² f (x³) dx.

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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: Suppose f(x) is a function defined in an open interval containing the number a. One of the most…

A: The given statement Suppose f(x) is a function defined in an open interval containing the number a.…

Q: If the graph of function f(x) contains the following points: X -2 0 1 4 y 2 -1 3 -5 Which of the…

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Q: 2-x lim x→1 (x − 1)²

A: The given limit is .The aim is to find the limit value.

Q: + 7. y₁ = x² - 4x + 3 Y₂ = =x² + 2x + 3 y

A:

Q: Q2: Find the inverse Laplace Transform of each of the following: K d) 5s-3 s²+4 - S $²+9 35+2…

A: (c) Given that

Q: Determine whether the equation is exact. If it is, then solve it. e'(9y-5t)dt + (2+9e¹) dy=0

A: Given differential Equation is as follows

Q: For a first-order DE like  ����=�(�,�),  what is an equilibrium value?   Question 1 options:…

A: The objective of the question is to understand the concept of an equilibrium value in the context of…

Q: Determine the derivative of with respect to x. g'(x) = g(x) = √ 12x² + 4x+2 + 9 (8x - 11)5

A: To determine the derivative of the following function with respect to .

Q: Find the horizontal asymptote of `f(x) = (2 x+5 x^3+4)/(-5 x^3+3 x^2+1)`

A: The objective of this question is to find the horizontal asymptote of the given function f(x) = (2x…

Q: Given point S(0, 1, 1) and 4y+3z=-12, find the distance from the point to the plane.

A: To find the distance of the point (0,1,1) from the plane 4y+3z=-12.