Use the transformation x = au and y = bu to find the area of an ellipse with equation + = 1. (Hint: If you understand what is going on, this problem does not need an integration to be performed at all!)

Q: 1. a = (2, 5, −4), b = (1, −2, −3) 2. a = (-1,0, 2), b = (3, 4, −5)

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Q: Find the vertex form of the function. Then find each of the following (A) Intercepts (B) Vertex (C)…

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Q: 3 Use algebra to find the point at which the line f(x) T- 4 59 6 h(x)= - Y 4 3 C Write the values of…

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Q: Evaluate. n=1 2n+4 7n

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Q: Find the points on the curve where the tangent is horizontal or vertical. You may want to use a…

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Q: Q9: Showthat triangle ABC is right at A where A(1,0,1), B(2,1,0), c (1, 2, 3).

A: Question No. (9):To show that triangle ABC is right at A where . Note: Since the student has posted…

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Q: Suppose a triangle in space has vertices (a, b₁, ²₁), (a₂, bz, C₂) and (93, b3; (3). Explain how you…

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Q: 1) State the order of the given ordinary differential equation. Determine whether the equation is…

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Q: Profit The profit P (in dollars) made by a cinema from selling & Bags of popc x² 28,000 3,300, 0≤x≤…

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Q: 5 4 --3- 2 -1

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Q: (b) Use the Fundamental x² :) = ( 4 – t) 1 F(x) = S(4 Chly appr Theorem of Calculus to calculate…

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Q: A radar gun was used to record the speed of a runner during the first 5 seconds of a race (see…

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Q: Find the general solution of the ODE: y' y²-6y+10 = 1 =

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Q: Exponential Growth: a. The table below represents an exponential function. Find the missing values.…

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Q: Find the general solution of the first-order linear equation dy dx + 2y = e²x

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Q: Consider the following differential equation to be solved by the method of unde y" + 2y = -18x²e2x…

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Q: a. b. C. Find the derivative of the function. y = sin(tan(7x)) Find the derivative of the function.…

A: According to Bartleby answering guidelines, we can answer only first three subparts. Kindly post…

Q: Use spherical coordinates. Evaluate xex + y2 t2 + dV, where E is the portion of the unit ball x² +…

A: To find  E is the portion of the unit ball  that lies in the first octant

Q: Is the series convergent or divergent? If convergent, is it absolutely convergent? cos (πn) e-n COS…

A: Consider the series

Q: If 1800 square centimeters of material is available to make a box with a square base and an open…

A: Let the side of the square base = x cmLet height of box = y cm

Q: 2) Draw a direction field for the given differential equation. Based on the direction field,…

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Q: Find an equation of the tangent line to the graph at the given point. (y - 3)² = 4(x - 5), (6, 1) y…

A: The tangent to a curve at a point is obtained by finding the slope at that particular point using…

Q: Use upper and lower sums to approximate the area of the region using the given number of…

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Q: b) Consider the triangle formed by the side of the house, ladder, and the ground. Find the rate at…

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Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

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Q: Determine the inverse Laplace transform: F(s) = 4/s2 - 5/(s + 1)

A: To determine the inverse Laplace transform.

Q: Labor. Refer to Table 4. (A) Find the average rate of change of weekly hours from 1980 to 1990.…

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Q: Find all values of x and y such that f (x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = x² +…

A: The given function .The aim is to find all values of  and  such that .

Q: (a) Find parametric equations for the line segment that joins the point P(-1, -4,-3) to the point Q…

A: Question no. 1(a):To find the parametric equations for the line segment that joins the point..Note:…

Q: 1. Using the fundamental theorem of calculus part 1, along with properties of the definite integral…

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Q: Determine if the series diverges. If it does diverge, type a upper case D as your answer, and if the…

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Q: Seperate the variable and solve the equation 2y (dy/dx) + 2x = 0. Use the initial condition x = 0;…

A: The given equation .The aim is to find the solution with the initial value .

Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

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Q: Find the area of the shaded region. y 3 2 1 (1, 1) 2 y = ³x y || 4 1 X 6 X = 8 CO 8 X

A: Given equations of the curve

Q: Find the first partial derivatives of the function. f(x, y) = 7xy fx fy -

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Q: Find a formula for the nth term of the sequence where an is calculated directly from the value of n.…

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Q: 2. Consider 1, 0.1, 0.01, 0.001, 0.0001, ... (a) Write out the next three terms of this sequence.…

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Q: Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the…

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Q: Evaluate the double integral [[ (zy + 2) dA, where D is the set of points contain within the corner…

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Q: Find the surface area of the part of the plane 2x+5y+z=4 that lies inside the cylinder x^2+y^2=1.…

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Q: For the following integral, (a) sketch the corresponding area, (b) approximate the area using the…

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Q: Differentiate the following function to review unit two. a. b. C. d. 11 11 y = ²+1 4 - 3t² + 2 F(x)…

A: y=t2+1t4−3t2+2Take derivative.y′=ddt(t2+1t4−3t2+2)Use the quotient rule for the derivative:…

Q: If what are the bounds of integration for the first integral? a= 11 [ f(a)d= = [ f(x) dx + " f dx […

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Q: 3. a. Find the intervals of increase and decrease for the following. y = 2x² - 8x + 1 b. y=x² + 160…

A: A function f (x) increases in the interval I if f'(x) > 0 for all x in I.A function f (x)…

Q: Let (a) (b) (√x + ²) dr + (y² + ln(2x)) dy=0, x>0. Check that this is an exact differential…

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Q: 1. If y2 = 10x, then A. - 5 2xy 1 C. -2232 2x d² y dx2 = B. D. - 1 5x 2y 5xy 2

A: Given,

Q: Find aw/as and aw/at using the appropriate Chain Rule. Values Function w = y³ - 2x²y s=-3, t = 6 x =…

A: To find  by using the appropriate Chain Rule.Function: Values: To evaluate each partial derivate at…

Q: (a) Find parametric equations for the line segment that joins the point P(-1,-4,-3) to the point Q…

A: Question no. 1(a):To find the parametric equations for the line segment that joins the point .Note:…

Q: Evaluate the integral by converting to polar coordinates. 3 S³ S 0 9-x² cos(x² + y²) dy dx = 0

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