Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the unit vector u = cos ei + sin 0j. f(x, y) = P(2, 0), A = - 6 9x + y

Q: 2n Let an = 3n +5 Determine whether {an} is convergent. Determine whether an is convergent.

A: To determine whether the given sequence and series is convergent or not.

Q: b. f(x) = x - 3 x² – 9 2-

A: The given function is,   f(x)=x-3x2-9

Q: Let v = (5,1,-2) and w =(4,-4,3). Calculate v w.

A: Given,v=5i+j-2kw=4i-4j+3kWe know that if (a1i+b1j+c1k).(…

Q: b/ Find the solution to the homogeneous differential equation below dy x²+y² dx 2ху

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Q: Use Lagrange multipliers to find a vector in 3-space whose length is 8V3 and whose components have…

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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Q: Determine if the following statement is true or false. The lines L1 and L2 are skew. L:x = 10 + 3t,…

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Q: Find all solutions of the system of equations. (If there is no solution, enter NO SOLUTION.) S 3x² -…

A: topic - linear equations in two variables

Q: 12. A. If possible, give an example of 2 divergent sequences an and bn such that E(an + bn) has a…

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Q: Determine whether the lines L1 and L2 are parallel. L: x = 2 – 31, y = 4 +1, z = 7- t L2: x = 5 –…

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Q: 8 16 22 63 26 51 75 29 67 LIt rained 35 inches last year. This year, it rained 19 inches. How many…

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Q: Suppose at t minutes, r(t) meters is the radius of a circular oil spill from a ruptured tanker and…

A: The given data is: rt=4t2+20,    if 0≤t≤216t+4,     if t>2 To prove that r is continuous at 2.

Q: 31. *7/2 csc t cot t dt

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Q: What is the x-intercept of the tangent line to y=ln(x) with a slope of 8?

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Q: Integrate: (7x³ + 4x²) dx

A: Given:- ∫(7x3+4x2)dx

Q: Use Lagrange multipliers to find the minimum value of the function f(x, y) = x2 + y? subject to the…

A: Given f(x,y)=x2+y2 and subject to constraint is xy=2 and we need to find the minimum value of given…

Q: Determine whether the lines L and L2 are parallel. L1: x= 2-3t, y = 3+ t, L2: x = 4- 12t, y= -3 +…

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Q: Solve the given differential equation by separation of variables. dy − (y − 2)2 dx = 0

A: Given

Q: Sxšel-x®dx 1–x6

A: Find your answer below

Q: JI (x - 1)5 + 3 (х — 1)? + 5 Jdx

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Q: Evaluate the integral of x(x – 5)1²dx with limits from 5 to 6.

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Q: 6 arcsin(sin 40 ) = _____. -40° -220° 40° 220°

A: Solve the following

Q: 2T 26. cos e de

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Q: Find the composite functions (f • g) and (g ). What is the domain of each composite function? (Enter…

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Q: Given f(x) = 1 –(5+ 10x) + (5 + 10x)² – 27 (5 + 10x)³ then f'(x) =, %3D - (5 + 10z) – ( 5 +…

A: f(x)=1-32(5+10x)+94(5+10x)2-278(5+10x)3 Then f'(x)=0-(32×10)+(94×2×5+10x×10)-(278×3×(5+10x)2×10)…

Q: 1 cos(sec-x) dx 2/V3 xVx²-1

A: Let's find.

Q: o S(e*+3 + ex-3)dx +e*-3•

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Q: 4 Simplify arctan 5 + arctan 6 (round to the nearest degree). 21° 159° 201°

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Q: 3 dx extle) Vx+4 V x+4

A: Explained below

Q: Evaluate the sum. 30 E(5j + 4)° j=1 (Give your answer as a whole or exact number.) 30 Esj + 4)° =…

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Q: 4х if х> -1 f(x) 3D { 5 — х2 if b < x<-1 Зх + 7 if x < b

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Q: 30. | (Зи — 2)(и + 1) du

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Q: Find the inverse of the matrix of the following [1 8 91 1-A=|0 4 6 Lo o 3] 2 [3 2- A=5 -1 3

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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: Evaluate the iterates integrals r*dA D = {(r, y) : 1 <I< e, 0Sys In(r)}

A: Given problem:- ∫∫D x3 dA        D={(x, y) : 1≤ x≤ e, 0≤ y≤ ln(x) }

Q: (a) x = 6t,y = - 7+ 4t O (x, y) = (0, 6) + t{ – 7,4) ai + bj = -7j + t(6i + 4j) O (x, y) = (0, 7) +…

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Q: Зх — у 3 4 -2x +y = 5 - %3D

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Q: D = {(r, y) : 1 <Ise, 0<yS In(r)}

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Q: ) If we apply Rolle's Theorem to the function f(x)=2x^2−8x−4 on the interval [0,4], how many values…

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Q: 7) Find the radius of convergence and interval of convergence of the following series: (х — 2)" | n²…

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Q: 10. Find the first partial derivatives of the following functions (it is not necessary to simplify).…

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Q: Please answer each question with solution.

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Q: Let a = ci + jand b = 2i + 10j. Find c so that a and b are orthogona C = i

A: Given: a=ci+j b=2i+10j.

Q: 3 ex dx,n = 10 х, п 1

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Q: Use synthetic division to show that x is a solution of the third-degree polynomial equation and use…

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Q: Two equations and their graphs are given. Find the intersection points of the graphs by solving the…

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Q: Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: topic - vectors