For f(x,y)=-6x'y° : (a) Determine fx(x,y) . 6.6 Answer: -42x (b) Determine fy(x,y). Answer: -36x 7.5 'x

Q: Convert the Cartesian equation x 2 + y 2 - 6x = 0 to a polar equation.  r² = 6cosθ r = 6sinθ r =…

A: The given Cartesian equation x 2 + y 2 - 6x = 0 ................................... (1)

Q: ° Fis defined by f(x)%3D 2°(x + 4) on increasing (enter intervals in ascending order)? ion is…

A:

Q: The graph of the function g(x) = sin (x) is shown. Use the graphing utility to sketch the graph of…

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Q: Given the area of the region enclosed by y = 4 – x' and y = -x+2, identify the BOTTOM function.

A:

Q: Write the integral that would be used to find the area bounded by y = x2 + 1, y = x - 2, x = -2 and…

A: Given y=x2+1,  y=x-2, x=-2 and x=2

Q: D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item,…

A:

Q: If the following series converges, compute its sum. Otherwise, enter oo if it diverges to infinity,…

A: Find your answer below

Q: b. g = f(t, v) = tv, t = In m v = m

A: We can solve this as follows:

Q: dx 4. x²+4x+13

A:

Q: Find real numbers a and b such that the equation is true. a + bi = 2+6i a = 3,6 = 2 a = 5,6 = 9 a =…

A: To find the values of a and b.

Q: By separating variables, find the general solution of the differential equation dvc = - dt RC' where…

A:

Q: Evaluate the following integral: •Vx+4 sin(y – 3y?) dy Jx+4 | 2

A: First we integrate the given function and then we put limit and simplify.

Q: Write the quotient in standard form. 4+i 4-i

A: 4+i4-i

Q: y = (1+) - (1+)*

A: We have to find dy/dx for the given function.

Q: Cases and Complements 1. A group of four animals will be selected for adoption from a group of 10…

A:

Q: 1(x) (х+1)* II

A: follow the procedure given below.

Q: Consider the following. t = − 4?/3 (a) Find the reference number t for the value of t. t =    (b)…

A: We have to find the reference no t and terminal point determined by t.

Q: Use Mean-Value theorem to find c X +2x-1 ; [o,i] xj[3,5] Use L'Hôspital vule to find the wmit lime…

A: We will solve the Problem on limits and mean value theorem.

Q: Evaluate: J 1+sinx -dx

A: To evaluate the given integral.

Q: Find the amplitude and period of the function. y = 3 + 1/2 cos(?x) amplitude=           period=…

A:

Q: A large company has installed new robotic equipment in its assembly areas. This new equipment…

A:

Q: D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item,…

A:

Q: 1. f(x) = x

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: the area of the region enclosed by y = 2 – x´ and y = -x, identify the "a" and "b"

A:

Q: If k is any real number, prove or disprove that sinkx 1. lim x→0 kx 1.

A:

Q: The cost of producing q units of good is C(q) 0.1q2 +3q+ 100 pesos. The firm can sell q units when…

A: This question can be solved using the concept of derivatives and rate of change of quantities.

Q: lim (n + 1 – Vn² n) n 00

A: Given query is to find indicated limit.

Q: Evaluate the following limits. If needed, enter INF for o and MINF for -0. (a) It – 9 lim t²+5t +5…

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Q: Find the solution. dy 31 +9y=2ty 5/3 dt

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Q: y = (x-p)(x-r) and p+r=6. Find the x coordinate of the vertex of the parabola. O a. None O b. 6 O c.…

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Q: II. Given the function g defined by g(x) = -* if x*-2 4. if x=-2 Find the value of the indicated…

A: at x=-2, function is defined as:g(x)=-4;       if x=-2ANSWER 14:g(-2)=4

Q: ax +3, if x<2 bx² +2, if x 22 f(x) =- It is given that f(1 and f(2) = 6. Find the value of f(a+b). O…

A: We will put all the values to find the values of a and b .

Q: 13 Convert x 2 + y 2 - 2x = 0 to a polar equation. r = 2cosθ r² = 2cosθ r = 2sinθ

A: We have to find the polar equation

Q: x=r +1, y=r -t uation of the tangent to the curve at tl Show all your work.

A:

Q: Choose the point which shows the correct location for the polar coordinate (2, 57). 90 WIN 135 45 1…

A: We will use the concepts of Cartesian coordinates.

Q: Let f''(x) = 2x + 4 and suppose f'( – 1) = 6 and f(– 1) = 3. Find f'(x) = and find f(3) =

A: Given,            f"(x) = 2x + 4,           f'(-1) = 6,           f(-1) = 3

Q: 4. When the graphs of two functions intersect the angle of intersection is defined as the angle…

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Q: sin 2n Determine whether the sequence defined by a, %3D 9n converges or diverges. If it converges,…

A: We have to find limit

Q: the

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Q: 3t Using standard Laplace transforms, find Laplace transform F(s) for cos (G)

A: f(t)=cos23t2using:cos 2x =2cos2x-1f(t)=1+cos23t22f(t)=12+cos 3t2F(s)=L12+Lcos3t2

Q: The inflection point of the function f(x) = x³ – x² + 5æ + 1 is: (금, 꽃) 70 3 (-3, – ) 70 (-;, ) 27…

A:

Q: A theorem states that one local extremum implies absolute extremum. Verify that the following…

A: A(r)=12r+3πr2 , r&gt;0SupposeA'(r)=0(-1r2×12)+6πr=0-12+6πr3=0 ⇒r3=126π⇒r3=2π⇒r=2π3

Q: Prove or disprove. If the substitution u = f(x)dx becomes g(u)du, and if an indefinite integral of…

A: Given problem:- Prove or disprove. If the substitution u = Ø(x) is such that f(x) dx becomes g(u)du,…

Q: Approximate the area under the graph of f(x) 1 over the interval (0, 4] using five rectangles. x +1…

A: Let's find.

Q: y=x, 4x +y“ = 12

A: The region is bounded by the curves,    y=x, 4x+y2=12

Q: Find the differential of the given functions: 1. y = 3x4 - 5x³ + x - 4 2. u = /2y – y3

A:

Q: x²+6x , |2x-4 , x<a Find all values of a such that the function, g(x)= is continuous xz a…

A: g(x) is continuous everywhere if it is continuous at x=a as…

Q: TT sin 5. Approximate dx by Simpson's rule with seventh ordinates?

A: Simpson's Rule:    ∫abf(x)dx=∆x3f(x0)+4f(x1)+2f(x2)+...+2f(xn-2)+4(fn-1)+f(xn) Where, ∆x=b-an We…

Q: Show that the production function f (x) = - () x3 + 10x? + 5x, -∞< x< ∞ has both a concave and…

A: Find your answer below

Q: amplitude: period: phase shift: 6.

A: Follow the procedure given below.