An object moves on a trajectory given by r(t)=<10cos4t,10sin4t> for 0≤t≤π.

Q: Find f'(a). f'(a) = f(x) = 3x²5x + 1

A: The given function is

Q: a kite 65 feet above the ground moves horizontally at a speed of 8ft/s. at what rate is the angle…

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Q: 3x²+1 -dx (x+1)(x − 5) ²° AST A. B. I cos (3x cos (3x) sin(5x) dx

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

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Q: Find the inverse, if it exists, for the given matrix. - 3 -1 4 1 Select the correct choice below…

A: The given matrix is,

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 8x² 6 dy =

A: Given function is y=8x2 -6

Q: The graph of fis shown in the figure. Sketch a graph of the derivative of f. -6 -5 -4 -3 -2 Select…

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Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

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Q: Find the vertex, focus, and directrix of the parabola. ​(x+3)+(y-1)^2=0

A: The given equation of parabola

Q: A patrol car is parked 35 feet from a long warehouse (see figure). The revolving light on top of the…

A: A car is parked 35 feet from a long warehouse. The revolving light on the top of the car turns at a…

Q: The function f is defined as f(x) = 2e4x². (a) Find f'(x). f'(x) = (b) For what value of x is the…

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Q: USE INTEGRATING FACTORS I. Find the General Solution: Answer is already given. 3. y' = x - 2y Ans.…

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Q: Find u x v, v x u, and v x v. | = (−1, 5, 4) v = (-5, -4, -7)

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Q: Differentiate. y = dy dx In x11 12 4

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Q: Differentiate the function y = √7-x using the Chain Rule. dy dx = 5

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Q: Evaluate the following iterated integral: 2 2 8-x²-y² [² [²[**²-³ xye²² dzdydx.

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Q: The initial value problem (t²-81) y" - 8ty' +8y= In (t²) y(-11) = 5 y'(-11) = 5 has a unique…

A: Now to find the undefined points, take the denominator equal to zero.

Q: use the linear approximation of f(x) = sqrt(16-x) at a=0 to approximate the values sqrt(16.1) and…

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Q: Evaluate each limit analytically. - (a) lim sin(x + h) – sin(x) h→0 h (b) lim h→0 (c) (d) lim h→0…

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Q: Sketch the region bounded above by the curve 2e-* sin(πx), the x-axis, and x = 1, and find the area…

A: We find the area of the region bounded by and the the x-axis, and x = 1.

Q: sinx Evaluate lim- x 0+x Evaluate lim x-0 Evaluate lim 10+x Evaluate lim 0+x 3x - sinx and enter…

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Q: USE INTEGRATING FACTORS I. Find the General Solution: Answer is already given. 14. ay my c₁emx,…

A: The given differential equation is; dy/dx - my = c1emx..

Q: 17. lim x-0 tan 7x nic sin x

A: Question no. (17):To evaluate the following limit.Note: Since, the student has mentioned to solve…

Q: 11 Find the derivative of f(x) = x¹¹. f'(x) = 5

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Q: The graph of a function is given; each grid line represents 1 unit. Use the graph to complete parts…

A: Domain is the value of x for which the function is defined. Domain of the function is : (-2,7) Range…

Q: Determine the derivative of the function k(x) = x6ï with respect to X. Ay

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Q: At what point is the tangent line to the curve y³ = 2x² perpendicular to the line x+y=2=0? NOTE:…

A: The given line is,The coefficient of x is -1 which means the slope of the tangent line is -1The…

Q: Set up an integral for the area of the surface obtained by rotating the given curve about the…

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Q: Differentiate the function. y = (2x² − x + 1) (-x5 + 3) y' = 5

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Q: Find the general solution of the given differential equation. dy X - y = x² sin(x) dx y(x) = Give…

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Q: The sum of the first 100 terms of the arithmetic series 3 + 1 + (-1) + (-3) + ... is

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Q: 25. xVy + y = 10; (1,8)

A: Given, .Given point is (1,8).

Q: For the following trajectory, find the speed associated with the trajectory and then find the length…

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Q: If 320, 240, 180, ... are the first three terms of a geometric sequence, then the value of the…

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Q: The weekly sales of Honolulu Red Oranges is given by q=81921p. where q is the number of oranges sold…

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Q: a kite 50ft above the ground moves horizontally at 9ft/s; at what rate is the angle between the…

A: This is question of calculus Here rate of change is given We have to find rate of change of angle…

Q: The population of the world in 2015 was 9.75 billion people and was growing at a rate of 1.25% per…

A: The given equation is,Where t is the number of years after 2015 and P is the population in billion…

Q: 1. In each part, find the dot product of the vectors and the cosine of the angle between them.…

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Q: Body temperature is usually maintained between 36.4°C and 37.4°C, inclusive. Determine the…

A: The temperature in degrees Celsius ranges 36.4o C to 37.4oCThe objective is to convert this the…

Q: Select EACH limit that allows L'Hopital's rule. Does not matter what the limit equals. Just want to…

A: we can apply L'hopitals rule to a limit if the limiting value is of the indeterminate form  For any…

Q: Find the area under the curve y = 2x -3 from x = 8 to x = t and evaluate it for t = 10, t = 100.…

A: ;

Q: Differentiate the following function with respect to : f(x) = √4+x² 5x f'(x) =

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Q: 5. Use the table of ordered pairs to determine the value of each composite function. f(x)=x²-15 g(x)…

A: f(x)=x2−15g(x)=xxf(x)xg(x)1−14112−11423−69341164510255621366734497

Q: Use the given values to evaluate (if possible) three trigonometric functions cos x, csc x, tan x.…

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Q: Polynomials and Rational Functions If P(x) and Q(x) are polynomials and Q(c) = 0, then ● ● limP(x) =…

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Q: Given the curve y = 2x - 5x + 3, find the slope of the secant lines between x = -2 and each of the…

A: Given the curve , to find the slope of the secant line between  and each  of the x-value in the…

Q: 29. Evaluate these questions involving asymptotes. a. b. Find the horizontal and vertical asymptotes…

A: Vertical asymptotes occur whendenominator is 0. , Equation of vertical asymptotes Degree of…

Q: gravel is dumped from a conveyor belt at a rate of 30ft^3/min; it forms in a shape of a right…

A: Gravel is dumped from a conveyor belt at a rate of  The shape is a right circular coneGiven the…

Q: ·N 2 v(t) @. 3 An object moves with velocity function v (t) = sin(t) during the time interval [0;…

A: The given velocity function  during the time interval

Q: Determine the length, to 1 decimal place, of the arc that subtends an angle of 1.5 radians at the…

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