(-1)" Given: In(1 + x) = En=0' tu+1 if |x| < 1. n+1 1. Find the Maclaurin series for f(x) = xln(1+;). 2. Evaluate f(2022)(0).

Q: Question 1 Given: xy = tan(a - y). Find dx/dy. %3D tan (z-y) sec (r-y)- " +tan? (-y) sec" (7-y) O dr…

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Q: Let a = ci + j and b = 12i + 16j. Find c so that the angle between a and bis- Round your answers to…

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Q: = -14 – 5t = -5t y = 21 + 3t = 5t – 43 Given the skew lines l1 : Y = 9 – t and l2 : = 2t – 7 (a)…

A: Since, you have ask a question with multiple sup-parts, as per company guidelines we will solve the…

Q: Find the vector component of v = (4, -1,7) along b = (2, 3, –6) and the vector component of v…

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Q: (a – x)°dx S(4x + 1)°dx

A: use the substitution method for solving the integral.

Q: Find X only using Crammers rule 2x+リ-「Z=D2 x2 -y +VZ 2 x? +2y +VN= 4

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Q: Find the directional derivative of the function at P in the direction of v. h(x, у, 2) %3D хуz, P(4,…

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Q: Find the directional derivative of f at P in the direction of a. f (x, y, z) = ry + z²; P(-4,–3,4);…

A: We need to find directional derivative.

Q: Find an equation of the plane that is parallel to the plane x + 7y – 2z + 20 = 0 and contains the…

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Q: Find the remaining trigonometric ratios. Зл T < x < 2 1 cos(x) %3D sin(x) tan(x) %3D %3D cot(x)…

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Q: 4. dx + (x – y + 2)?dy = 0

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Q: (a) Find an equation of the tangent plane to the surface at the given point. хуz %3D 10, (1, 2, 5)…

A: Given:  a)   The equation of surface is   F(x, y, z) = xyz – 10 = 0   given point =1,2,5 On…

Q: rection: Determine if the given function is continuous and differentiable at the indicated values of…

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Q: Test the series below for convergence using the Ratio Test. Σ 0.7 n=1 The limit of the ratio test…

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Q: 2x + 4 h(x) = 1 2x 1 f (x) = 1 –x g(x) = 3( x + 2x 6. | 3 -- 8. a.lim -4 · f (x) d.lim (8 · f(x) –…

A: Given:      fx=1-18x      gx=3x+2x6+4     hx=2x6-2x+13

Q: Find the vector component of v = 21 -j+ 3k along b = 4i + 4j + 7kand the vector component of v…

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Q: Either prove the following statement is true or provide an example to illustrate it is not true: if…

A: This question can be solved using the concept of even function.

Q: d dx

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Q: (2x - 5y + 3)dx - (2x+4y - 6)dy = 0

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Q: Find the simplified form of the derivative of y = 1+csc 3x %3D cot 3x O y = 3 csc 3x csc(3r)-1 O (E)…

A: We have to find the simplified form of the derivative of  y = 1+csc 3xcot 3x.

Q: Are the lines = 7+12t, y = 12–10r, z = 1+2t, and.x = 6+13t, y = 8+2t, z = 10–5t parallel? O No O Yes

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Q: Determine whether the lines Lj and L2 are parallel. L1: x = 3 – 4t, y = 5 + t, z = 8 – t L2: x = 5 –…

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Q: Evaluate the volume of the solid generated by revolving the plane region about an axis. Show…

A: We have to find volume of solid generated by revolving the plane region about an y - axis.

Q: d,e,f

A: We will solve the limits.

Q: Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not…

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Q: Find parametric equations of the line that satisfies the stated conditions. The line through (–3,0,…

A: We need to find Parametric equation.

Q: OQUESTION 14 Find the area enclosed by the given curves. y = 4 - x 2, y = x +2,x= - 2 and x = 2 O…

A: Given query is to find the area enclosed.

Q: Find the area of the parallelogram that has u = i – j+ 2k and v = 2j + k as adjacent sides. NOTE:…

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Q: Determine the sum of the series п(п + 2) n= if possible. (If the series diverges, enter 'infinity',…

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Q: Display all powers of 2 that are less than 20000. Display the list in a properly formatted manner,…

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Q: Find the distance between the parallel planes – 2x + y +z = 0 and 10r – 5y – 5z – 11 = 0. Note:…

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Q: Examine the function f (x, y) = x3 − 6xy + y3 for relative extrema and saddle points.

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = x² + y2 + z* (5,…

A: To find gradient of the function at the given point.

Q: Compute the following limit. 1-e3 3x as x approaches 0

A: To find,  limx→01-e3x3x

Q: 1. Let p be a positive number. Express cos(x)dx as a series, if possible. If not possible, explain…

A: To solve the following problem

Q: Integrate the following differential and determine the constant of integration: dy/dx = 8/x which…

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Q: 6" We want to determine if the sequence is monotonic. (3п)! Using the ratio test we get that n+1 Sn…

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Q: O f (x) = -6 sin(3x + 1) cos(3x + 1)ecos"(3+1)

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Q: 1. Which of the following is a convergent p-series? (A) n³ n=1 n (B) 3 n=1 1 (C) n=1 3 1 (D) n n=1

A: A) ∑n=1∞ n3     Since n is positive integer⇒  The above series diverges B) ∑n=1∞13n   It is not p…

Q: 2. (2x– 3y +1)dx - (3x + 2y – 4)dy = 0 |

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Q: 2. Determine the critical points, the maxima and minima, and the inflection points of the function y…

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Q: answer

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Q: Use any method to determine whether the series converges or diverges. 00 k + 27 k= The series…

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Q: Area = 2 Area = 1. Area = 3 3 5 7 Area = 7 Graph of f' The figure above shows the graph of f', the…

A: Note : As per our guidelines we are supposed to answer only three subparts if there are multiple…

Q: у %3D7 — х, у —D 0, х %3D 0, revolved at х ахis 2.

A: To evaluate the volume of the solid generated by revolving the plane region about an axis.y=7-x,…

Q: Given that Vf(12, – 7) = 9i – 4j, find the directional derivative of the function f at the point…

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Q: Find the vector component of v = 2i – j + 3k along b = 2i + 4j + 4k and the vector component of v…

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Q: 4x2 8(7x – 4) x(x+ 8)(x – 2) (x + 2)³ - f(r) = with f'(x) = and f"(x) = %3D (x + 2)2 (x + 2)4 a.…

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