3. Evaluate: lim x-0 (sinx

Q: The position of a particle in the xy-plane at time t is r(t) = (t - 1) i + ( - 2) j. Find an…

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Q: (x) = Vxcl

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Q: dy By using implicit differentiation, find dx x.y)-(1.0) for xy + e*» = sin(x +1). (x.y)-(1,0)

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Q: ne hundredth derivative of p (x) (x + x³ + x')1º (1 + x² )11 (x³ + + x Justify ya

A: P(x) = (x+x5+x7 )10(1+x2 )11(x3+x5+x7) Here, (x+x5+x7)10  will have x70 as leading degree. (1+x2)11…

Q: 3. a) Describe the translations applied to the graph of y= x² to obtain a graph of the quadratic…

A: Here we have to use the transformation of graphs.

Q: A hot air balloon rising vertically is tracked by an observer located 8 km from the lift-off point.…

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Q: If m s f(x) S M for a sxs b, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: Find the area of the region described. - 3 The region in the first quadrant bounded by y =x and y= 3…

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Q: Find the equation for the plane through the point Po = (2,7,6) and normal to the vector n= 3i + 5j +…

A: Given:-normal, n=3i+5j+6kpoint on the plane, P0=2, 7, 6let (x, y , z) on the plane vector (x-2)i+…

Q: y – 2. Suppose the symmetric equations of lines l1 and l2 are = 2 - y = z and a = -1, 2…

A: x-12=2-y=z implies L1 : x-12=y-2-1=z-01x=-1, y-23=z-12 implies  L2 : x+10=y-23=z-12If lines L1 and…

Q: Learning Activity 1: Determine the general antiderivatives of the following functions: 1. f(x)=6x5 -…

A: Solving the problems by finding the integration.   NOTE :: As per our Expert guidelines we are…

Q: x5Vx2 + 2dx

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Q: Assume that the radius r of a sphere is expanding at a rate of 70 cm/min. The volume of a sphere is…

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Q: .

A: We will find the derivative.

Q: eventually

A: We will solve the problem.

Q: 2. Evaluate ř(t) dt: 4 4t ř(t) t2 + 5t + 6' î + 2e4t cos t j - k; a = 0 and b = 4 t2 + 1

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Q: 16. lim (2 – 3x) = –4 x → 2 %3D - 19. lim (1-3-) -- 3 20. lim 2 = 7 x → 5 21. lim x2 – 2x – 8 = 6 x…

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Q: Find the point, P, at which the line intersects the plane. x= - 7+ 9t, y= -7-5t, z= 8- 10t; 9x – 9y…

A: Please refer to the image below

Q: Use Ring Method Rotate the region bounded by x = (y – 3)2 and x = 16 about the x = -5.

A: Let's find.

Q: 2 3. Evaluate the integral ||x dx -2 O 2 4

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Q: Find the arc length of y = +(x + 2)³ + (x + 2)-1 for 1 < x < 2. (Give your answer to three decimal…

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Q: Find an equation for the conic that satisfies the given conditions. ellipse, center (-3, 3), vertex…

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Q: Vx-a?

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Q: 2. Give the symmetric equations of the line l perpendicular to the plane T : 5x – 2y = z+4 and…

A: The vector perpendicular to the plane 5x-2y-z=4 is 5i-2j-k This allows us to write the point vector…

Q: 23. y = 2x, y=x, 0<x< 6

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Q: Solve ƒx² ln(x) dx using Integration by Parts. Use u = In(x) and v = x². Answer:

A: Given integral is  ∫x2ln(x) dx. we have to find the value of the integration using integral by parts…

Q: The slope of a tangent line at (1, 4) is 2. What is the equation of the line? Select the correct…

A: As asked we can answer the question with out all explanation in the following steps

Q: Find the deviva coulx ty)sy

A: Given query is to find the derivative of the expression.

Q: 2. Find the Area bounded by the curve y = 4-x? and the x-axis.

A: Topic = Area

Q: solve

A: We will solve the integral.

Q: Basic Coatalus 1. f(x) - f(xth) = 5(x +h) - 3 Sx - 3 lim 5(x+h)-3 [5x-31 56 +5h -3 - 5% +½ 1. lim…

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Q: (v) sin"x y = ne Inx? y = 1+x? (vi)

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Q: Use the root test to determine whether the series 7n -n-2\" 3n2 +n+ 4 converges or diverges. Since…

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Q: Find a parametrization of the line in which the planes x+ y +z = - 3 and y +z = 4 intersect. Find…

A: Solution: x+y+z = -3 ..............(1) y+z =4 .............(2)

Q: blem #1: Differentiatef (x ) = [(4 x4 -5 )(3 x2-9 x - 5 ) ]3 and solve f (2).

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Q: In Exercises, the given vectors form a basis for a subspace w of R' or R'. Apply the Gram-Schmidt…

A: We have to obtain an orthogonal basis for w.

Q: The rectangles in the graph below illustrate a left endpoint Riemann sum for f(x) = on the interval…

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Q: Find the curve's unit tangent vector. T(t) = Di+Dj+Ok

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Q: G'(0), where G(r) =| e * dt

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Q: Find the sum of the series. Σ 00 9hn! n = 0

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Q: FInd the Indefinte Integral and check the result by differentlation. 6x dx Step 1 s the derivative…

A: The given integral,          ∫6x8-x23dx

Q: The difference between two angles, how is the result of the same trigonometric function

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Q: Use implicit differentiation to determine dy/dx given the equation x^5+y^2=−4

A: implicit differentiation to determine dy/dx given the equation    x5+y2=−4

Q: rV4- a² dx

A: Let's find.

Q: Kndly answer immediately   If f ‘(x) > 0 for all x = (a, b), then function f in the interval is a.…

A: topic- derivative of function

Q: Use the method of disks/rings to determine the volume of the solid obtained by rotating the triangle…

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Q: 6. Find the intersection of the line I and the plane t. 1:7 = (4,–1,4)+t(5,–2,3) T: 2x+5y+z+2=0

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Q: Question 5 of 13 On what instance does the Chain Rule of differentiation applicable? Explain…

A: In this question we have to find on which instance does the chain rule of differentiation…

Q: (-1)" /n + I is n + 2 n=1

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Q: Show clear and detailed solutions: Suppose that z is a function of x and y, and tan Vy? + x² = z*e®y…

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