||r'(t) x r"(t)|| Use the formula k(t) : to find k(t). 3 r(t) = ei+etj K(t)

Q: 2r-4x2-x-3 dx x- 2r 3 In Ix+ 1 +3 ln|x-3| + C +1-3 ln|x-31+ C Option 1 Option 2 2 In |x + 1| - 3…

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Q: 1 19 9. -10 -k Consider the matrix it corresponds to an augmented matrixial representation of a…

A: To find for given conditions of alpha and k and the system have how many solutions.

Q: Verify Green's Theorem by evaluating both integrals aN aM dy dA ду ax for the given path. C: square…

A: Application of integration

Q: ind [r(t) · u(t)] and Ir(t) x u(t)] in two different ways. dt r(t) = ti + 5t2j + t³k, u(t) = tk (a)…

A: Solving

Q: Let be A, B, C three matrixes 30 1 B = z A = 2 y C = 5 13 -10, 10 What is the value for X that…

A: We will solve for x.

Q: A small resort is situated on an island that lies exactly 4 miles from PP, the nearest point to the…

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Q: Find the positive root of the equation x + 2x2 + 10x - 20 in the interval [1,2] using Regula Falsi…

A: Let, the given function be: f(x)=x3+2x2+10x-20 And, the formula of the method is:…

Q: x2- 2 (x+ 2)(x + 1)² x+2 (x + 1)2 x+2 (I + x) Option 1 Option 2 1 (x + 1)2 x+ 2 (x + 1)

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Q: y' + 4y = e^(4t) %3D

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Q: Find an arc length parametrization of r(t) = (e' sin t, e' cos t, le') r1(s) = (|

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Q: -2+0.5-0.125+...= (Write your final answer in fraction form, when applicable)

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Q: Find the sum of the following power series: 3 3.7 1+7** 4-8 3.7.11 3.7.11.15 + 4.8. 12 4.8. 12• 16…

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Q: 1. Find all relative extrema and soddle points of the functon Use econd Partials Test where appli…

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Q: Calculate r'(t) and T(t), where r(t) = (2t – 5, 4 – 4t, 1 + 4t). %3D r'(t) = { %3D T(t) = {

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Q: 8. Relationship Between Continuity and Differentiability: (a) Justification needed): If lim…

A: To discuss the  relationship between continuity and differentiability.

Q: 2.) S- e2x dx ex – 5

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Q: testconuer gnce and diverg ence 2+5 3"

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Q: 5x2+11x+2 dx x(x+1)²

A: integration using partial fraction

Q: Find the general solution of the differential equation. dy = xy + 3x dx

A: To find the general solution of the following differential equation.dydx=xy+3x

Q: dx V2+Vx-1

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Q: Determine the slope of the tangent to √1-x at the point (-8, 3).

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Q: 1. Given ä = (-2,–1,4),B = (5,2,3)and č = (-3,0,5) determine each of the followin a) ĉ b) |2ã – 7|…

A: As per our guidelines we are supposed to answer?️ only 3 question. Kindly repost other question as…

Q: For a plane curve r(t) = (x(t), y(t)), |æ'(t)y" (t) – x"(t)y' (t)| (x'(t)² + y' (t)²)³/2 - k(t) Use…

A: Here we have to use this equation to compute the curvature at the given point.

Q: Evaluate the following indefinite integral: x dx 1.) S - Vxt – 1

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Q: 1 If z = 2x2 – 3y with u = x² sin y and v = 2y cos x, determine expressions %3D az dz for and du

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Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. e-4x²…

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Q: Evaluate the limit: r(t + h) – r(t) lim h >0 for r(t) = (t°, sint, 1) h r'(t) = (

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Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y 0, y= 4+ x°…

A: Here we have to find the volume.

Q: Verify Green's Theorem by evaluating both integrals ON aM | y? dx + -x² dy dA ax ay for the given…

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Q: Use the first principles delta method to find the derivative of y = x2 – x. %3D

A: Here we have to find the derivative of y by using the first principles delta method.

Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). ||r(t)||* r(t) = t'i + t°j

A: Here we have r(t)=t2i+t5j We have to find κ(t)=r'(t)×r''(t)r'(t)3 ..................................…

Q: 2. True or False? a) -2(3BA)and 6AB'are equal vectors. Justify your answer. b) If |AB| = |AC|, then…

A: This question can be solved using the concept of equal vectors.

Q: 1. Solve for x, if 0 < 0 < 2n. Write your answers in exact values only. 2 2cos" x + cos x- 1 0

A: Given: 2cos2x+cosx-1=0  and 0≤θ≤2πlet cosx=mthen 2cos2x+cosx-1=0        2m2+m-1=0We know that root…

Q: v (km/hr) t (hours) -b The figure above gives your velocity during a trip starting from home.…

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Q: 4 fy 1 -3 -2 1 -1 -2

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Q: If f(x) = cos(2x) then find II f (t|4)

A: Given query is to find the Indicated derivative.

Q: 1

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Q: 5 + 5(-5) + 5(-5)' +.. 4 Σ. 4 i= 1 8.

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Q: A ball is launched straight up in the air from a height of 5 feet. Its velocity (feet/second) t…

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Q: Find the area inside the circle r = = cos 0, but outside the circle r = 1/2. Sketch the graphs first

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Q: (a) Use Green's Theorem to find the line integral over the simple, closed curve C : r(t) = (cos t,…

A: To use green's theorem to find the given line integral over the curve C

Q: Find curl (8z i + 9xj+4y k). curl(8z i + 9x j + 4y k) = ( i )i + ( i j+( i )k

A: topic- curl of a vector

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5- 5 -5+ -5+

A: Given data÷

Q: 17. y dx — (х + бу?) dy %3D 0

A: To determine the solution of the given differential equation.

Q: Find the domain, x-intercept, and vertical asymptote of the logarithmic function and sketch its…

A: We have to find out

Q: Area A = 1,427 Calculate the definite integral f(x) dx by referring to the Area B = 2,460 Area C =…

A: Here we will find the definite integral,

Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

A: To find the volume of the given solid using triple integral.

Q: A particle moves vertically (in inches) along the yaxis according to the position equation s(t) = -…

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Q: Find the area of the region bounded by the curves y = 1/x , y = x and y = 4x in the first quadrant.…

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Q: Prove the given identities. csc 0 – cot 0 (a) sec 0 – 1 = cot 0 (b) cot 0 + tan 0 = csc 0 sec 0 For…

A: a) [csc(theta)-cot(theta)]/[sec(theta)-1]=cot(theta) b) cot(theta)+tan(theta)=csc(theta)sec(theta)…