19. x - y² +3=0, x-2y = 0.

Q: Problem 2 What region R in the ry-plane maximizes the value of √√₁ (4-20² R Give reasons to your…

A: An integral of a function f(x, y) over an area in xy-plane represents a signed volume of the solid…

Q: a. Find the value of a for which the matrix A is singular, A = [97] b. Find the inverse matrix B-¹…

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Q: The constant solution y ≡ π/2 of the equation y' = cos(y) is stable , true or false ?

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Q: Two six sided dice are rolled, and the numbers are observed. What is the probability that the two…

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Q: 25. Let f(x) = 5x² + 1. Evaluate and simplify each of the following: f(4)-f(1) 4-1 (A) (Bu PC (B)…

A: Given function is we have to evaluate the following  and simplify them

Q: How close does the line y = 6 + 2x come to origin? The closest distance the line y = 6 + 2x comes to…

A:

Q: If f(x) = 2 - x / 5x , determine the equation of f^ -1(x) , the inverse of f(x).

A: Given, the functionWe determine the equation of .

Q: Maximize p = 2x + 3y + 5z 2y + 2y + Y + Subject To: 2x + X ++ X + IA IA IA 2 3x < z 10 15 40

A:

Q: Of all rectangles with a perimeter of 25, which one has the maximum area? (Give the dimensions.

A: We can find the dimensions as below.

Q: If A = (11) 01 " then eat = et tet et (& 0

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Q: Evaluate the definite integral. 6.² sin (4t)dt

A: Let assume,

Q: 27. Use spherical coordinates to find the volume of the solid cardioid of revolution D = {(p, 0,0):…

A: Solid is bounded by D={(ρ,ϕ,θ):0≤ρ≤(1−cos⁡ϕ)/2,0≤ϕ≤π,0≤θ≤2π}Using spherical…

Q: .f.xv 33. x√2x – 1 dx. -

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Q: sinx x0 e²x-1 5. Use power series to evaluate lim

A: Power series expansion

Q: 51. lim x³ = 1. x→1

A: To give an  proof for the following statement.

Q: Given: (x is number of items) 4800 Demand function: d(x) = Supply function: s(x) = 3√x Find the…

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Q: bok out $17000 in student loans. The loans are to be repaid over 10 years at a rate of 4.25%. Assume…

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Q: Find the present value of a continuous income stream F(t) = 10 + 3t, where t is in years and F is in…

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Q: Determine each feature of the graph of the given function. f(x) Y = Answer Attempt 1 out of 2 −5x² +…

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Q: Please solve the integral: f sec(x)^2 tan(x) dx two different ways: By letting u=sec(x), and by…

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Q: What is lim h→0 A. 3x² (x + h)³ = x³ ? h B. 6xh C. h² D. O

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Q: 6 Let g (2) = -3 cos (z) sin (2) Determine an indefinite integral of g. s - 6 3 cos (z) sin (z)dz

A: The given integration is

Q: Which of the following functions f: R → R is continuous at the point 0 € R? f(x) = x² = f(x): = {22²…

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Q: f's domain. x f(x) a b C d 1 2 4 8 Determine if f is invertible. O Yes, f is invertible. O No, f in…

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Q: csc csc(x) dx Expand fraction by csc(x) + cot(x): csc(x) (csc(x) + cot(x)) csc(x) + cot(x) 1² dx

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Q: Solve the exponential equation. Express irrational solutions in exact form. 41-9x = 3X What is the…

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Q: -5 -4 3 2 4 3 2 1 -2 -3 -4 1 on Use the graph of f(x) above to estimate the value of f'(0) to one…

A: Given: A graph of a function is given as follows:To find: We have to estimate  from the given graph.…

Q: The graph of f(x) = 2x³ + 12x² - 126x + 23 has two horizontal tangents. What is the negative value…

A: Solution-Now differentiate this function with respect of x,d/dx(f(x))=f'(x)

Q: Find the first partial derivatives of the function. ax + by CX + dy f(x, y) = fx(x, y) = fy(x, y) =

A: To find the first partial derivative of the function.

Q: the position vector of a particle is r(t). Find the requested vector. The velocity at t=4 for…

A: r(t)=(3t2+5t+1)i−6t3j+(4−t2)kUsing the power Ruleddxxn=nxn−1

Q: The intersection of two events E and F, denoted En F, is the event consisting of all outcomes that…

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it…

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Q: The equation y' = e^y has a constant solution, true or false ?

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Q: ff xdxdy where R is the region bounded by y = 0, y = 1, x = 2 and y=x

A: ∬xdxdyWhere R is the region bounded by y=0,y=1,x=2 and y=xy≤x≤20≤y≤1

Q: A kite 120 feet above the ground is being blown away from the person holding its string parallel to…

A:

Q: 3x - 6 Given a function is defined by f(x) = x² + 3x- 10 for what value(s) of x does the function…

A: f(x)=3x−6x2+3x−10

Q: Given f(x, y) = 4x6 – 6xy³ – 2y¹, find fz (x, y) = fy(x, y) =

A:

Q: 29 (-2,2) Find the equation for the parabola that has its focus at the equation is ,2 and has…

A: Given that Focus is at S

Q: Use the graph below to answer the question. B no E Oyes H Is vertex H adjacent to vertex A? F

A: The graph is given as,

Q: The solution of the initial value problem y'= y^(2) − 1, y(0) = 2 is defined on the entire real…

A:

Q: Consider f(x) = (x + c cx² +5 for x < 3, for x ≥ 3 For what value of the constant c is f continuous…

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Q: Find all x-intercepts of the following function. Write your answer or answers as coordinate points.…

A: f(x)=(x2+11x-12)

Q: Find the volume of the region between the cylinder z = 5y2 and the xy-plane that is bounded by the…

A: Recall:

Q: Find all vertical asymptotes of the following function. f(x) = 2x² 128 x² 17x + 72

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Q: The equation of the hyperbola that has a center at (4, 10), a focus at (-1,10), and a vertex at…

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Q: (a) A = 20º, b = 11, c = 7

A: (a) Given thatNow, we are using the law of cosines

Q: 231 Evaluate the integral (x²yz + xy²z + xyz²)dzdydx 010

A:

Q: The figure below shows the graph of f. Use the figure to answer -7-6-5-4-3-2- -21 4321 122 4 5 6 2 8…

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Q: Compare the graphs of y=f(x) and y= f(2x): A) y=f(x) is reflected in the y-axis  B) y=f(x) is…

A: To compare the graphs of .

Q: Explain why an exponential or logarithmic function would not be used to model the graph from…

A: An exponential or logarithm function cannot model the graph, because the graph is not monotonic.