of the following indicates that the graph of the function f(z) has a horizontal asymptote th(") and ("") m₂+2+ f(x) = +00 im₂++ f(x) = ther (") nor ("")

Q: 32. a. b. f cos(4sinx - 1) cos(2sinx + 8) cosx dx is sin(6sinx + 7) − sin(−2sinx + 9) + C 1 1 12. 1…

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Q: Region R is bounded by the graphs of C₁ : x = y + 1 and C₂: x = 3 - y² as shown in the graph below.…

A: Given: Region R is  bounded by the graph x=y+1 and x=3-y2 as shown in question. USE: cylinders…

Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

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Q: Find the derivative of the vector function, r(t) =

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Q: = √ Evaluate 1 /x(1 + √x)² dx.

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Q: Apply Newton's Method to f(x) and initial guess xo to calculate x₁, x2, x3. f(x) = x² - 13, xo = 4…

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Q: Let y=tan(4x+6)  Find the differential dy when x=1 and dx=0.1  Find the differential dy when x=1…

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Q: is

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Q: Find the coordinates of a point P on the line and a vector v parallel to the line. x − 3 _ y + 1 4 2…

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Q: If limx-5 f(x) = 4, limx-5 g(x) = 2, and limx-5 h(x) = 18, what is the value of lim x-5 4f(x) + g(x)…

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Q: Let f: [1,1]→ R be a function given by f(x)=2x-x2. Then the inverse image (preimage) of [0,4] under…

A: The answer is option D

Q: if a = (3, 2, 9) and b = (-4, 7, 2), find a • b.   a) a • b =-9   b)  a • b = 19   c)  a • b =…

A: In this question we have to find the value of a·b

Q: Match the functions in Column A with their corresponding antiderivatives in Column A a. F(x) =…

A: Let's find antiderivative of function c.

Q: Choose the domain of the following function f(x, y)= ln(2x - y - 5) O None of the others O D = {(x,…

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Q: A rental company charges $65 a day and 20 cents a mile for renting a truck. Michael rents a truck…

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Q: 1 . Find the arc length for y = √√2-x² for 0 ≤ x ≤ √√2. Check your answer by noting that the curve…

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Q: Book Design A book designer has decided that the pages of a book should have 1 in. margins at the…

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Q: y'' + 8y' + 32y = 0, y(0) = 4, y'(0) = -24 y(t) = The behavior of the solutions are: O Oscillating…

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Q: Solve ODE (1 + x²)dy + (xy + x³ + x)dx <=0

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Q: Find all vertical and horizontal asymptotes of the graph of the function. (Enter your answers as a…

A: This question is based on vertical and horizontal asymptote.

Q: Two cars start moving from the same point. One travels south at 60mi/h and the other travels west at…

A: We have to find distance between two car

Q: What is the instantaneous rate of change at x = 2 of the function f given by 2x f(x) O O 4 -2 H N -…

A: What is instantaneous rate of change at x=2 of the function f given by   f(x)= 2x/x-1

Q: f(x, y) = Find fx, fxy, and fxyx. 7 8x+5 + 8x³ e-8y

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Q: Minimizing Packaging Costs A rectangular box is to have a square base and a volume of 36 ft³. If the…

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Q: Let A = A(r) give the area of a circle of radius r. The instantaneous rate of change of the area as…

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Q: with the initial condition y(1) = 4. -0 Y

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Q: (x¹+y¹) dx - xy³ dy = 0 [Answer: y = 4x¹logx + Cx¹]

A: This question is based on Homogeneous differential equation.

Q: Find the difference quotient for each of the following functions and reduce to lowest terms A.…

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Q: 1 √√1/₂ 1/² y+4 y² + y fip C

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Q: Given that lim f(x) = -7 and lim g(x) = 6, find the following limit. X-3 X-3 lim X-3 2-f(x) x+ g(x)…

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Q: Part c: ( 1. Find the gradient of the function f(x, y, z) = ln(xy) - zx² at the point (1, 1, -1). 2.…

A: We have to find the gradient and directional derivative.

Q: Evaluate (i) dx S √e xlnx√(2lnx)² – 1

A: We are asked to evaluate the integral

Q: Determine whether the series Σ or divergent. +∞0 (-1)" 4" 100 is absolutely convergent,…

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Q: Use the table of Laplace transforms to find the Laplace transforms of the following functions. a)…

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Q: A police car is located 40 feet to the side of a straight road. A red car is driving along the road…

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Q: 1. (x² + y² + 2x) dx + 2ydy = 0

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Q: Determine whether the lines L₁ and L₂ are parallel, skew or intersecting L₁: x = 4 + 2t, y = -5 +…

A: L1 : x=a1+b1t , y =c1+d1t , z=e1+f1tL2 : x=a2+b2s, y =c2+d2s , z=e2+f2sthen Lines L1 and L2 are…

Q: Which of the following statements must be true? 1. If f is differentiable, then II. If f is…

A: Solution of given question is written in below steps.

Q: Find dy dr dy dr for y = ㅇ 2 5+ 6t dt.

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Q: Question 1 described by the vector function r(t) = (4t² ln t, t-4 29 -2e-³t). a) Find the integral…

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Q: For the curve f(x) = Find the horizontal and vertical asymptotes. x-4x² +2 x² - 4x +4

A: We can solve this as follows:

Q: If u = (0, 2, 3) and v = (1, 3, -1), find the projection of u onto v. 이름다 a) Obl 이유ㅎ ○ c) (1, 1, -1)…

A: This question can be solved using the concept of vector projection of a vector on other vector.

Q: 4. Compute dx S in two ways and verify that the answers agree.

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Q: 6. If z = x + iy = (x, y), then the equation z²+z+ 1 = 0 is written as (x,y)(x, y) + (x, y) + (1,0)…

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Q: 9 -8 -7 y=x+2- 3 4 5 7 8 9 10 Find the average value of f(x) = x + 2 on the interval [1,4]. Hint:…

A: The average value of fx=x+2 on the interval 1,4

Q: Find a parametrization r(t,s) for the plane which contains the point P(-9, 7, 1) and the line…

A: Use plane concept

Q: 18 (x² +9) (x+3) -dx

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Q: For the curve f(x) = Find the horizontal and vertical asymptotes. x-4x² +2 x² - 4x +4

A: This question can be solved using the concept of horizontal and vertical asymptote of rational…

Q: fe* sin 2xdx.

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Q: Let f be a continuous function with f'(x) = 3x² Of has no relative maxima. 0x=0 0x=2 0x=1 - 6x. At…

A: f be a continuous function with f'x=3x2-6x