2. Find the domains of the functions f(x, y) = ln (x² − y) and g(x, y) = 14 y²-x²

Q: Find (gof)(-2) if f(x)+x^2+3 ; g(x) 2x-5

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Q: A; B; Evaluate the expression without using a calculator. Expand and simplify. (2x + 3)² C; Solve…

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: Use an appropriate substitution to solve the differential equation ² ( ² ) ) dx - + cos² - X dx - x…

A: we need to find out the solution.

Q: 7. dg+q=4 cos 2r; q(0)=1. dt

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Q: Evaluate the integral dx ✔ -x+8x-12 0 dx 2 -x+8x-12 &

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Q: 4. Let In = f cos" xdx. Show that: In = 1 - Cos' n on-1 x sin x + n-¹ In-2, n ≥2. n

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Q: Find the limit as →∞ and →∞. Use this information, together with intercepts, to give a rough of the…

A: The given equation is y=x3(x+2)2(x-1) We have to find the x-intercept and y-intercept

Q: 4. Use implicit differentiation on these. a) Find an expression for dy/dx at any point on the curve…

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Q: he graphs of y = f(x) (solid) and y = g(x) (dashed) are shown. The two graphs intersect at ( Region…

A: Topic:- application of integration

Q: ) Given the piecewise defined function f(x) = {10x b) lim f(x) (10x-5,x<3 3x², x ≥ 3 c) lim f(x) a)…

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Q: x² x where a = b = Consider the indefinite integral x¹ + 25x² Then the integrand has partial…

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Q: Maximize f(x, y) = √11-x² - y², x + y - 2 = 0.

A: The given function to maximize is: f(x,y)=11-x2-y2 with the constraint g(x,y)=x+y-2=0...(1)

Q: Use an appropriate substitution (4-5 a cos² to solve the differential equation (-) ) ª dx - x dy =…

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Q: 8) Given two planes P₁:2x+4y+3z=4 and P₂:x-y-2z=-3 (a) Let L be the line of intersection of the two…

A: Given Planes :- P1: 2x+4y+3z=4 P2: x-y-2z=-3

Q: Graph and find the vertical asymptote of the function: x² +1 3x-2x² y =

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Q: h(x) = (lx - 21 (4- 2x if x # 2 if x = 2

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Q: i) f 3x +2x?+x dx *

A: given that, ∫3x3+2x2+xx dxwe know that,∫xn dx=xn+1n+1+C

Q: The temperature T at a point (x, y) is T(x, y) and is measured using the Celsius scale. A fly crawls…

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Q: Graph the function f(x) = x^2 - 2x/ 2x^2 - 3x -2 Please name any x-intercepts or y-intercepts…

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Q: 1 y = f(x) EV 5 4 3 لیا 2- 1 y 0 1 2 lim z 6 lim z 3+ f(x) = f(x) = 3 Enter each answer as a whole…

A: Need to find out the following limits.

Q: Find particular solution of the differential equation in the attached  image

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Q: h(x)= (1x - 21 14 - 2x if x # 2 if x = 2

A: Given: At x=2, h(2) = 0. So, the function can be written as h(x)=|x-2|. And the function is…

Q: (c) Give one example where the Green theorem fails, and explain how.

A: Green's Theorem

Q: If m ≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: JL=28 KL=5x+6 JK=3x+6 Find KL

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Q: 5. Change of variable 2 x dx 3x+1 a.

A: Given function, ∫12x3x+1dx

Q: Use the second derivative test to identify any critical points and determine whether each critical…

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Q: -4 -2

A: We have to find the following conditions according to the given information

Q: 2. The height of a golf ball after t seconds given by s(t) = 24t - 4.9t2 meters. (a) Find the…

A: This is a problem related to derivative of the function. Please follow the procedure given below. As…

Q: 3. f(t) = 3t - t², (0,0) 4. f(x) = 3-5x, (-1,8) 5. g(x)=x²-9, (2,-5)

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Q: Evaluate the integral. x+7 2 x² +64 dx

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Q: 3. Use grad h(-3,4)=5ī +3j and h(-3,4)=10 to answer the following questions. a) Find the…

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Q: direction: find the indefinite integeal   x-3  / x^2 + 1

A: Given query is to find the integral.

Q: Let D = {-4, √6, 0, 2, 6.5, 10, 0.4, n}. Which elements of D are real numbers? (Select all that…

A: Real number:-It called father of number because it contain all numbers i.e it contains rational ,…

Q: 12. If $5000 is deposited in a bank paying r% interest (r = interest rate), the amount 3 years later…

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Q: Find the solution of the given DE. 5. y' +6xy=0; y(n) = 5.

A: The given differential equation is; y'+6xy=o, y(pi)=5.

Q: Find the solution of the given DE. 1. y' + y = xy(1) = 0, x

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Q: Find y" by implicit differentiation. 4x³ + 3y³ Зу3 = 4

A: Quotient Rule of differentiation : ddx(uv) =v.dudx-u.dvdxv2.

Q: 8⑧1+S 1+ (+)+ +8

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Q: Price(q) = 10300 * 0.780.119 +0.119². Find the quantity that minimizes price

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Q: Green's Theorem (a) State the Green theorem in the plane. (b) Express part (a) in vector notation.

A: We have to do A and B.

Q: b. 14-x²|dx

A: I am attaching image so that you understand each and every step.

Q: For this discussion post, I will ask you to sketch some graphs that meet a limit condition and…

A: To be found - Sketch of different functions with given conditions. Topic - Function, limits &amp;…

Q: The graph below is the function f(x) 3 2 OF -5-4-3-2-1 Find lim 24-1 Find lim 24-1¹ Olim f(x) 2411…

A: As x tends to Right side f(x) tends to -1 , therefore limx→-1-f(x)=-1

Q: K Use the following function and its graph to answer parts (a) through (d) below. Let f(x) = 4-x, x…

A: Limit of a function exist at a point c when left hand limit equal to right hand limit equals to f(c)…

Q: Graph the function  f(x)= -2x^3 + 4x^2 + 2x - 4 Please name any x-intercepts and y-intercepts in…

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Q: On a routine inspection of the water system of Cincinnati, Fernanda discovers a pipe leaking at the…

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Q: x³-1 lim x+1√√x-1

A: Given; Limx-1 (x3-1)/(sqrtx -1).

Q: 1. Basic Integration a. fx(x + 1)dx b. S √ √x+x² dx x C. √₁²|x-1|dx

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Q: (x⁹ + x4)dx (x5 - 5)10

A: