Use polynomial division to express the following rational functions as a quotient plus a rational remander R(x)=3x^3-2x^2+5x-7 / x+2

Q: lim x-x6-x O +∞ 00 ∞- O O 3 1 2 ||

A: topic - limits

Q: Region A is bounded by the parabola x = y², the line y = 1, and the y-axis. Region B is bounded by…

A: As per the instruction, we will be answering the first question. Given: We need to find the volume…

Q: Activity 6.1.3. In each of the following problems, our goal is to determine the area of the region…

A:

Q: If then fxx = Select one: True False 2(y² + y) (y - x)³ f(x, y) = x + y² y-x

A: According to question,Given Function,fx, x = x + y2 y-x

Q: f (x-2)(x+1)' dx

A:

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

A:

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: Write the system of equations 3x 2y4z = -3 5x + 5y + 4z = 1 - 4x + 5y + 4z = 3 as a matrix equation,…

A: Given: equations: 3x-2y-4z=-35x+5y+4z=1-4x+5y+4z=3matrix equation is AX=BA[xyz]=Bwe can write the…

Q: Work Problem for the question. Let where x = t = -1. You must provide a clear and detailed solution…

A: Please see the below picture for detailed solution.

Q: Let Find fa, fay and fryz f(x, y) =In(xy)-26x¹0 y 10

A:

Q: √x +3 If f(x, y) = xy +7 the domain of f(x, y). Select one: True O False then the point (1, −7) is…

A:

Q: 1 2 x² +6x+18 -dx

A: A detailed solution is given below. We know that, ∫dx(x+a)2+a2 =  1a tan-1x+aa + c

Q: Find the gradient of the function at the given point. w = x tan(y + z), (7, 15,-5) Vw(7, 15,-5) =…

A:

Q: Find the area bounded by y = 4x -x^2 and x = 0, and y = 4 using two methods (vertical and horizontal…

A:

Q: Work problem 2 (1 Let w(x, y) = 5x - 5y - x² + 5y³, x = cos(t) and y = -sin(3s). Use chain rule to…

A:

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

A: This question is based on Homogeneous differential equation.

Q: If In (x² - y) -x+y+1 then the domain D of the function f is given by the set Select one: f(x, y) =…

A: Given function:- f(x,y)=lnx2-y-x+y+1  find domain of f(x,y)

Q: ax+ 2 x ≤ 2 f(x)=4-x², 2<x<3 2x+b. 3 < x Find the value of a so that f(x) is continuous at 2. Find…

A: To find out the value of a as f(x) is continuous at 2.

Q: Evaluate: 12+3 2√x+3 ○1-3 ln (7/5) O2-3 ln(7/5) 2 O2+3 ln7 03-In()

A:

Q: 3. f Arctany dy 4. fx(2x - 1)'dx 5. fycsc²ycoty dy 6. fxsin4xcos4x dx

A: The given integrals are;  5) y csc2y coty 6) x sin4x cos4x.

Q: (z In z + 5)dz

A:

Q: A police car traveling south toward Sioux Falls, Iowa, at 160 km/h pursues a truck traveling east…

A: Using the Pythagoras theorem for the figure: Let, z be the distance between two vehicles. We have:…

Q: swer of the following lim 2x²+6y² lim (x,y)→(0,0) x²+y²

A:

Q: 18. If A = 6 a. d. 14 5 0 10 10 1 14 0 01 7 0 b. 0 11 16 C. 8 9 12 14 3577 NOV00 7 572 7 6 7 1 2 61…

A: In this question we have to multiply Matrix.

Q: 3. (ey + 1) cosx dx + eysinx dy = 0 [Answer: (ey + 1) sinx = c]

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: f(x, y) a b) = 4x²+2y² Find the domain of f. Show that the limit does not exist lim f(x,y) (x,y) →…

A: Here, the given function is: f(x,y)=3xy4x2+2y2

Q: Question a) b) Let f(x, y) = 2√x - y²e-²xy + ²². Find fx and fy. Evaluate fxxy(4,-1).

A:

Q: find the rate of change of the circumference of a circle when the area is increasing at the rate of…

A:

Q: 3) [3 Consider the DE: -(4x³y – 16)dy = (6x²y² – 10)dx. A) Show that the differential equation is…

A: For a differential equation Mdx+Ndy=0  to be exact if ∂M∂y=∂N∂xand solution of a exact differential…

Q: d. graph y = f(x-2) e. graph y = f(x)+3

A: We have to draw graph as instructed in question.

Q: The domain of the function f(x, y) None of these This option D= {(x,y) = R² + +1} This option. D=…

A: We want to find the domain.

Q: 01. |x2 - 1\dx = a. b. 2 C. 432 - 23 23 d. 틀-

A: This question can be solved using the concept of definite integrals and modulus function.

Q: 4. ff 3 dx dy 0 y

A:

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

A: Solution ) to find the point p (x - 3)/4 = (y + 1)/2 = z + 4  = 0 (x - 3) /4 = 0   ,   (y + 1) /2  =…

Q: 2 +81 1/s(3² +9) ²0 ds

A: The given integral is (s4+81)/[s(s2+9)].

Q: Both rectangular form and polar form are used to represent the same complex numbers. Explain, using…

A: I have to explain why we are using different coordinate system.

Q: Determine the vector equation that represents the curve of intersection between the cylinder 2¹² +…

A:

Q: Let z = √√√7xy +9y, and x = s³ and y = 1². Use Chain Rule to find dz when t = 1 and s = 2. ds

A: To find out the given partial derivative.

Q: A road perpendicular to a highway leads to a farmhouse located a = 1.5 km away. An automobile…

A: This question is based on application of derivative.

Q: if g(x, y) = yln(x) - x²ln(2y + 1) then 9x (2,0) = 0 Select one: O True O False

A:

Q: Một chuyển động có phương trình: R(t) = (cos(4t))i + (sin(4t))j + 4tk. Tìm vector tiếp tuyến đơn vị…

A:

Q: 2. If z = x+iy = (x, y) then (2,-3)(-2, 1) is A. (1,8) C. (-1,-8)

A: Given,             z = x + iy = (x,y) To find   (2,-3)(-2,1)

Q: 3. Arctany dy

A:

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

A:

Q: Let z = (y - 2x) ³, where x = s′ s²t and y = st². Use the Chain Rule to dz find when s = 2 and t =…

A:

Q: Relative to an origin O. the points A. B. C have position vectors i. J+k. i+j+0k. respectively. The…

A:

Q: 2x² sin x + 3y³ 3x³ + 2y² lim (x,y)→(0,0) if we approach along y-axis, we will get Select one: True…

A: This question is based on two variable limits.

Q: Find the radius of convergence, R, of the series. 00 Σ ( + 9)" 97 In(n) n = 2 R = Find the interval,…

A:

Q: The area of the region enclosed by the two curves y=x²-4 and y = x - 4 is given by

A:

Q: Which is not the about f(x) = |x|? Continuow at O no targent line at 0 Derivative from left at O is…

A: Use the function value to evaluate which one is false