Question 8 The position vector r(t) = (4cos(t), 7 sin(t), 51²) describes the path of an object moving in space. Find the velocity v(t) of the object.

Q: valuate the following double integral over the region R by converting it to an iterated integral. Se…

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Q: Select the correct steps when differentiating from first principles. O a. O b. O C. O d. lim 0+x lim…

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Q: What is the equation of the sphere whose center is at (0, -3, 8) and with a radius of 5? Select the

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Q: nd an equation of a plane passing through the following 3 points (1,-1,-1), (-4,1,4), (3,5,3)

A: topic- equation of plane through three points equation of plane passing through three points…

Q: Prove, using integration, that the volume of a sphere with diameter "d" is πYd³ 6

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Q: The temperature at any point (x, y) in a steel plate is T = 900 -0.7x² - 1.1y2, where x and y are…

A: topic- partial differentiation

Q: Find the volume of a sphere pyramid of height "h" and base edge of length "a"

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Q: f(x)=x²-16x³ +61x² + 8+2i is a zero Part: 0/3 Part 1 of 3 +112x-476

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Q: w = sqrt(25 - 4x2- 4y2),  x=r cos(theta),  y=r sin(theta) (a) Find del w / del r and del w / del ?…

A: If w=f(x,y) ; x=g(r,θ) and y=hr,θ then           ∂w∂r =∂w∂x.∂x∂r+∂w∂y.∂y∂rand…

Q: Σ(−1)n n² + 2n + 3 5η3 + n + 1 n=1 11.

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Q: Find the radius of convergence, R, of the series. R = Î n = 1 I = n2n Find the interval, I, of…

A: We have to find out interval of convergence

Q: Given: f" f(x)dx= 36, [ f(x)dr = 12, 2. Find the ff. numbers: So a. C. f(x)dx b. [ (2f(x) + +12g(x)…

A: Explained below

Q: Find the definite integral that will compute for the area of the region bounded by y = ex, y = 0, x…

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Q: Differentiate implicitly to find dy/dx. cos(x) + tan(xy) + 4 = 3

A: The given function,   cosx+tanxy+4=3

Q: At how many points do the curves r₁(t) = ((t + 1)², — t² − 2t, t+2) and r₂(t) = (1 – t², t, t) -…

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Q: given u = and v= find 2u+5v

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Q: Find the volume when the following region is rotated about the y-axis: y = √4x², y = 0, x = 0.

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Q: Find the solution of the differential equation that satisfies the given initial condition. dp dt 7√…

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Q: e −1 -1 lim (−1) t⇒0 t

A: Use limit expansion

Q: 1-). 25 2-) 3+4i 3-1

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Q: Use a sum or difference identity to find the exact value of the expression. tan 75°

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Q: x) = = ph f and T3 on the same screen. y 2+ -1.0 -1.0 -0.5 -0.5 1 -1 -2 -3 y 2+ 2 1 -1 -2 -3 0.5 0.5…

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Q: y' = 2xy²

A: Given: y'=2xy2We need to solve the above differential equation.

Q: Solve the given initial-value problem. y(x) = y" + 6y' - 7y= 11e²x, y(0) = 1, y'(0) = 1 2x 7e -7.x +…

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Q: Find the trigonometric integral. (Use C for the constant of integration.) [" (cos(20)) (sin(0) +…

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Q: 8. n=1 (−1)n-1 n². 2n (error] < 0.0005)

A: Solve by adding partial sums

Q: Use the figure below to find the exact value of the trigonometric function of angle A. sin(A) 00 7 A

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Q: Use the given substitution to express the given radical expression as a trigonometric function…

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Q: a. b. C. Evaluate the following double integrals: (2xy + 3y²)dydx (r)drde (e-²) dydx (Changing the…

A: We need to evaluate the given double integrals. Please see below fora detailed answer.

Q: Use the figure below to find the exact value of the trigonometric function of angle A. sin (A) 6 A…

A: it is very basic question of trigonometry.

Q: A store finds that its sales revenue changes at a rate given by S'(t) = -30t² + 400t dollars per day…

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Q: d.) s 2x+3 x243x-1 dx

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Q: 3. Evaluate the definite integral below: S¯¼ √x² + 2x − 5dx + Sq − √x² + 2x − 5dx

A: To solve the following integral problem

Q: Solve the given initial-value problem. y" + 6y'7y= 11e²x, y(0) = 1, y'(0) = 1

A: Given :y''+6y'-7y=11e2x

Q: Let g(u) be a function such that f g(u) du = ln (1 + 8u²) + C. Evaluate fxg(x²) dx.

A: This question can be solved using the concept of integration by substitution and definite integrals.

Q: Question 3 a) b) [ Find the limit, if it exists, or show that the limit does not exist. lim…

A: a)limx,y→0,07x2+2y2yb)limx,y→0,049x2-98xy+49y27x-7y

Q: 1 3 (a) √ 2²³ + + + √²+2rdz [: x° 2x dx X (ln(x))² (b) / X dx

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Q: · F(x) = 5* (S₁²¹6 (√₁+ u²) du) dt

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Q: Question 6 Find the indefinite integral below. (3³¹-5sin - 5 sin(5t)j +15cos(5t)k)dt Do not include…

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Q: Find the general solution to: dy X xẩy = xảy x²y d y = o y = Cet² ° y = Cezx² ○ y = ex² ez x² + C…

A: We need to find out the general solution of the differential equation.

Q: A baseball leaves the hand of a pitcher 6 vertical feet above and 60 horizontal feet from home…

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Q: at f" si sin rdr = 2, find the average value of the sine function on the interval [0.7]. Also, find…

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Q: Find the exact values of sin 20, cos 20, tan 20 and the quadrant in which 20 lies. tan 0 = sin 20 =…

A: Solution of given question is written in below steps.

Q: ind the angle between the vectors u=, v=

A: Given that u=1,1, v=-5,3To find :Angle between two vectorsSolution…

Q: If n(A) = 106, n(A ∪ B) = 141, and n(A ∩ B) = 46, find n(B).

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Q: (d²4)(d - 2)y=0

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Q: Find the critical points of the given function. a) f(x)=√x²-4 b) f(x)= |3x +21-1

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Q: Question 3 Find a vector-valued function, using the given parameter, to represent the intersection…

A: We need to find r(t).

Q: Use the half-angle identities to evaluate exactly. sin 112.5° sin 112.5° = (Simplify your answer.…

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Q: P 2. Sketch the parametric curve and eliminate the parameter to find the Cartesian equation of the…

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