1. Express A = (3, 1, –1) as B+ C, where B is parallel to the vector (1, 4, 2) and C is perpendicular to the vector (1,4, 2).

Q: Consider the following. f(x, y) = xy2 4 r= 4 r= 3 (a) Set up an iterated integral in polar…

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Q: A ball is thrown vertically upward with a speed of 15 m/s. Determine the maximum height and the time…

A: Find maximum height and time to reach that's height

Q: O Question 17 Evaluate the integral dx (7x2 + 1) by making the appropriate substitution: dx = (7x2 +…

A: Solving

Q: 3. Consider the curve given by y2 = 4xy +1. %3D dy A. Find dx B. Find all points on the curve where…

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Q: dy da = y+ Vx² – y? O y = x cos(ln|æ|+ C) O y = x sin(n|x| + C) sin-1 (를)-In|미=C coS-1 (2) -Inl피 =C

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Q: I. Evaluate the following. You are NOT allowed to use L’Hopital's rule. Vx² – 2x – 3x 3 - V11+ 4x 2x…

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Q: O2/ Find all Max. Mn. Saddle point for the function Lelowr lay) = 2xy-5x-2y" + AX+4y-4 %3D

A: Maximum , Minimum and saddle points for f(x ,y) :   For critical points , fx(x,y) =0 = fy(x,y) (say)…

Q: for In (x + x?) dx

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Q: following functions fo - VE+3 and glo) = Find the formula for eXx) and simplify your answer. Then…

A: For f(x)=x+3 and g(x)=x+42, Our Aim is to find the formula forg∘fx and domain for g∘fx.

Q: Find the vertical asymptote(s) of the graph of the function. -2 3. (0) -+3)

A: Find vertical asymptotes

Q: Evaluate the integrals for 16 sin²x cos²x dx

A: ∫16sin2xcos2x dx=∫4(4sin2xcos2 x) dx                                 =4∫(2sinxcos x)2 dx…

Q: 1. Find the determinant of the given matrix. 1 0 4 -6 2 5 3 -1 2 3 2 1 -2 31 det A

A: Given :A=104-62503-123521-23

Q: For the following function, find its inverse. f(x)= In(6x 2)

A: Given, f(x)=ln(6x-2)

Q: Consider the function f(x) = : x2. (a) Find the intercepts of the graph of f (if any). (b) Find the…

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Q: Compute the given integral. fain' sin" x cos xdx +C

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Q: Find two positive angles and two negative angles that are coterminal with the given angle and less…

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Q: 1) Use the Integral Test to determine whether the series is convergent or divergent. п (Зп — 1)2 c)…

A: Given problem:-

Q: Determine dyðx Calculate the instantaneous rate of change of g at the point (4,1,2) in the direction…

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Q: Find an eigenbasis and diagonalize. (Show the details.) 101 72 9. -144 -103.

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Q: 7. Su° (4 + u°)°du

A: The objective of the question is evaluate the indefinite integral.

Q: Maximizing construction costs The management of the UNICO department store has decided to enclose an…

A: answer is in next step

Q: -3 0 5] 1-3 0 5 18) 00 0 1 1 00 0 0 0 A) 5 B) 4 C) 3 D) 2

A: Consider the matrix

Q: Problem #5: In the equation f (x) = e* In(5x) – e* + log find f '(3).

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Q: 1- v extends from (0,0) to (-3,2). Vector W extends from (0,0) to (-3,5). a- Find the magnitude of V…

A: This is a problem related to vector. Based on the general formula and concepts we will answer the…

Q: 1) A box containing a group of balls (blue and red) totaling 25 balls. If nother Five blue balls are…

A: Topic:- probability

Q: Find global maximum and global minimum of æ3 – 9x? – 48x + 52 on the interval [-5, 12]

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Q: why discontinuous  if lhl and rhl are same zero

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Q: The functions h(x) and h'(x) are not differentiable at x = 0. The graph of h has a point of…

A: Follow the procedure given below.

Q: Find the integral of f(3x2 + 4x + 1)*(3x + 2)

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Q: Find the derivative of cos(3x) O -3sin(3x) O 3sin(3x) O 3cos(3x) O -3cos(3x)

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Q: (b) Solve the following first-order ODE xy'y=2x* +2y*

A: Given that ODE                 xy3y' = 2x4 + 2y4 We can write this equation as   y' =2x4+2y4xy3…

Q: y+8y+5 (y-1)(y+1)(y2+8)2 Integration by Partial Fractions

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Q: Which of the following is false? O none 3 n The series >, is divergent. 6+n n=1 00 1 The series is…

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Q: p1 Use a straightedge to draw line

A: answer is in next step

Q: Find all solutions to the equation. 2 sinx- cosx=1 Write your answer in radians in terms of t, and…

A: Given: 2sin2x-cosx=1   As we know that; The general solution of the trigonometric equation cosx=cosα…

Q: Find the divergence of the following vector field. F= (3xyz, - 2xy z, - 4xyz?) %3D The divergence of…

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Q: Question 14 Use part I of the Fundamental Theorem of Calculus to find each derivative, given the…

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

Q: A curve is defined implicitly by the equation ax + by2=r2 Given that a=20, b=2 and r=7, find the…

A: We have to find the solution.

Q: If the derivative dx (instead of .) exists at a point and dx = 0, then the tangent line at that…

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Q: Find the vertical asymptote(s) of the graph of the function. 4. *+ Br + 15

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Q: for In (x + x) dx

A: A detailed solution is given below.

Q: n²+4 2(-1)n-1 2 n=1 n²+ 3

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Q: A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 63°C, it…

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Q: For j(z) = (3x2 - 7) (-2x* + 7x), find j' (x) by applying the product rule. Provide your answer…

A: j(x)=(3x2-7)(-2x3+7x) The product rule is: (fg)'=f'g+fg' From above:  f(x)=3x2-7g(x)=-2x3+7x Now,…

Q: Given the following vector field and oriented curve C, evaluate F•T ds. F= (-6y,6x) on the…

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Q: csc² 20 cot 20 de

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Q: "he following series is convergent: (8")(10") (7")(9") + 1 n=1 elect one: OTrue OFalse

A: Topic:- sequence and series

Q: Use Lagrange Multipliers to solve the following: Maximize f(x, y, z) = 4x + 2y + z subject to r² +y…

A: Max   f(x,y,z)=4x+2y+zsubject to x2+y+z2=1

Q: J(x+h)-f (x) h 4x+9x+5 Problem #1: Using lim, Find the slope of the tangent line y = 3x-8 at x = -1.

A: Given: y=4x3+9x+53x−8 Let f(x) =y=4x3+9x+53x−8 We know that f'x=limh→0 f(x+h)−f(x)h Now slope of the…

Q: a) [. :l: Determine whether the following series (-1)"5"-1n . 42n+1 n=1 is convergent or divergent.…

A: As per policy only first question is answered. Please refer to the image below