Question 1. A critical point of the function g(x, y) = ey + 3x²y-y is (0,0). Use the Second Derivative Test to classify this critical point. Show all your work!

Q: If f f(x) dx = 3 and I. III. [f(x)g (x)] dx = −6 III only I, II and III I only O II only g(x)dx =…

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Q: Let [ f(x) dx = 5, -6 Find and -3 [ f(x) dx = -4.5 -4.5 -3 6 (5 f(x) - 6) dx = f(x) dx = 6, f(x) dx…

A: The given integrals are;  f(x) , limit from -6 to -1.5. f(x), limit from -6 to -4.5. f(x), limit…

Q: r = 7e0.70 ¬ the interval 0 ≤ 0 ≤ 1 and the straight line egment between its ends. -ea =

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Q: Find the minimum and maximum values of z= 9x+4​y, if​ possible, for the following set of…

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Q: Find the slope of the line, and sketch its graph. 7x-6y=42 Find the slope of the line. Select the…

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Q: Use the quotient rule to evaluate h'(a) for the given function h(x) and a. 7x 9 - 2x Provide your…

A: A detailed solution is given below.

Q: (2) Find an expression for the area under the graph of f as a limit. Do NOT evaluate the limit. g(x)…

A: given :   g(x)=x+lnx

Q: 17. A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the…

A: Concept of similarity along with derivative is used.q

Q: a) 4x² +9y² + z² = 36 b) x² - y²z² = 1 c) x² +100y² - 36z² = 100 d) z = z= 2x² - 4y² e) x = z² - y²…

A: d)

Q: f(x)=2x-7 and g(x) = -18 Given (a) Find (fog)(x). (b) Find (gof)(x). (c) Is the operation of…

A: Given :fx=2x-7gx=1x

Q: Use the matrices below to perform matrix multiplication. If the operation is undefined, enter NA. BD…

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Q: A region bounded by f(y) = √√√y, y = 4, and x = 0 is shown. What is the volume of the solid formed…

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Q: Consider the graph of y = f(x) shown below in blue. Find the open interval(s) where f'(x) is…

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Q: Find the solution of the initial value problem y" — 2y' – 3y = 6te²t, y(0) = 1, y′(0) = 0. NOTE:…

A: We have to solve the given differential equation.

Q: Using the Inverse Function Theorem, what is (-¹) (8) given that f(x)=√6x-2? Note that (11) = 8. (Do…

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Q: -a cos y + ze-1/(1+y²), then If f(x, y, z) = el- of ?x ; |(1,0,п) = fæ (1, 0, 7).] (Show solution.)…

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Q: Please determine if the sequence converges or diverges. \left(\frac{n!+6}{n!-2}\right)

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Q: Which equation could be represented by the number line? A. -9+8 = -1 B. -4+ (-5) = -9 C. -1 + (-9) =…

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Q: For the function f(x) = (5x² − 2)4 determine the second derivative in factored form.

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Q: Solve the following linear programming problem.   ​Maximize: z= 39x+10y subject​ to: 8x+6y ≤48…

A: Given that, Maximize: z= 39x+10y subject​ to: 8x+6y ≤48   13x+y ≤48…

Q: Classroom activity 9.1 the monthly income earned by each of the following workers paid by the hour…

A: We have to determine the monthly income.

Q: 5. Find the area of the region bounded by y=x² - 6x +5 and the x-axis. 125 (a) A= square units 3 (b)…

A: To find the area of the region bounded by given curves.

Q: Determine the area enclosed by y = from x= -3/2 to x = 1. |- 1 x+2 and y = (x + 2)²

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Q: Use the properties of the definite integral to express the definite integral of ƒ (x) = 6x³ − 4x² +…

A: Given :f(x)=6x3-4x2+2x-3interval [ 1, 3 ]

Q: Solve the differential equation: dx dy + x = e-y.sec²y

A: Here we have to solve the differential equation.

Q: Solve the system of equations by any method. -3x+6y= 27 x - 2y = -9 Enter the exact answer as an…

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Q: Solve using Inverse Operaators. y"" - y' = 4e-x + 3e2x; Particular Solution: Y=C₁+ C₂ eax + C3 ebx…

A: See the details solution in below

Q: ४ = (y3/2/3) - y¹/2 from y = 1 to y = 9

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Q: ƒ(s) = 4s - 18 9-s² What function f(t) has Laplace transform: 5s (s - 2)² +

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Q: a. Write the equation of the line that represents the linear approximation to the following function…

A: Using linear approximation at x=a L(x) ≈f(a) + f'(a)(x-a)

Q: Q4\A: Find area of zone bounded by curves y = x² y = 2x+8

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Q: Find the coordinates of the points of inflection for the function. 14) f(x) = 7e-x²

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Q: 4. For the series Σ=1+()", does it converge and if so what does it converge to? * n²

A: We have to check that series 1/2*(2/5)n  where n=1 to infinity. Is convergent or divergent.

Q: x² - xy (x,y) (0,0) √√√√y If it exists, find lim Answer: .Write DNE of the limit does not exist.

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Q: Q2.B. A bag contains 19 tickets numbered from 1 to 19. A ticket is drawn and then another ticket is…

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Q: Refer to functions p and q. Evaluate (qop)(x) and write the domain in interval notation. Write your…

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Q: 2 1 Lotes So I+ y² xyer² 0 1+ 0 Evaluate Select one: ○ In 2 O ln 2 O 1/4 ○ In 2 O 1/2 O 1 -dydx.…

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Q: Find the area of the region bounded by y=x²-6r+5 and the z-axis. (a) A- 125 3 square units (b) A (c)…

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Q: Assume that the random variable X is normally distributed, with mean μ = 70 and standard deviation…

A: To find the probablity P(X>a)  then we have to convert the expression into  Z-score value of the…

Q: 16. Integral Ydy 6y2-1

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Q: Find the area bounded by r = cos 0 for -π/2 ≤0 ≤π/2.

A: Area enclosed by curve r=f(θ), α≤θ≤β is given by  Area = 12∫αβr2dθ

Q: (a) Find the slope of the line through (-7,5) and (9,-3). (b) Based on the slope, indicate whether…

A: Given :Points : -7, 5 and 9, -3

Q: 1. If f is a function, then limf(x, y) = f(2,5). (z,y) →(2,5) 2. If lim f(x, y) = 0, then lim f(x,0)…

A: Answer 1. False

Q: Solve using Inverse Operaators. y"" - y = 4e-x + 3e2x; Particular Solution: Y=C1+ C₂ eax + C3 ebx…

A: Given that,

Q: Since the creation of a social program, the percent of persons 65 years and over with a family…

A: Here we have to us ethe given function.

Q: If we know that g is a derivable function such that g'(81) = 6 and f is a function given by f(x) =…

A: Given :f(x)=gx4g'(81)=6

Q: Penny can see the clock on the top of her town’s courthouse from her front yard. The clock is at a…

A: Given:  horizontal distance from her front yard= 140 m            if the angle of elevation from…

Q: hid. The line y d. The line y = -5/8 -5/8 redbuthents 2 y 0 X = ochiul 14 4 X = - y² 2 1 y² dibel 2…

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Q: Evaluate the following antiderivatives. S dx √x²+2x+5

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Q: Determine where the function discontinuous. [-(x+2)² +1→x≤-2 f(x)=x+1→-2≤x≤3 [(x-3)² −1→x>3 Using…

A: the given function,  f(x)=-x+22+1,x≤-2x+1,-2≤x≤3x-32-1,x>3