Find and classify the critical point of f(x,y) = -³y² - xy + y²³.

Q: Question 12 Find the 2nd derivative (y") of y=√x ln x In 2

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Q: 8. Use that (1+x)-2 = 1-2x+3x² - 4x³ + for -1 ≤ x ≤ 1 to find the first four nonzero terms of the…

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Q: Apply Newton's Method to f(x) and initial guess xo to calculate x₁, x2, X3- f(x) = 1 – 5x sin(x), xo…

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Q: Let R be the region between the curves x = 36- y² and x = y² - 36. (a) These curves intersect when y…

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Q: 1. Given f(x) = x² + 7x + 12 and g(x)=x²-9 Find (f+g)(x), (f-g)(x). (f g)(x), and ()(x). 2. Given…

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Q: Use Newton's method to approximate a root of the equation cos (x² + 4) = 2³ as follows. Let x1 = 2…

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Q: The annual number of passengers going through Hartsfield-Jackson Atlanta International Airport…

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Q: The admission fee at an amusement park is $1.50 people entered the park, and the admission fees…

A: Given: The admission fee at an amusement prk is $1.50 for children and $4 for adults.On centrain…

Q: The figure has a tangent line drawn at a labeled point. c(t) thousand chips 8 6 4 2 (1.95, 7.07 0.5…

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Q: 3) [ Consider the DE: -(4x³y - 16)dy = (6x²y² - 10)dx. A) Show that the differential equation is…

A: Given :-4x3y-16dy=6x2y2-10dx

Q: Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of…

A: The given geometric sequence: 32, 38,332,.....

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Q: meª (In x)-5 Find: What is the behaviour of y as →→ ∞ ? Given: Y- ▬▬▬ Oy -∞ Oy →∞ Onone of the above…

A: Please see the below picture for detailed solution.

Q: Farmer Jones and his wife, Dr. Jones, decide to build a fence on their farm. Because Dr. Jones is a…

A: Follow the procedure given below.

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Q: B a A b LI Use the right triangle and the given information to solve the triangle. a = 1, c= 2; find…

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Q: If f'(1) = 4, f(1) = 2, and g(x) = f(x) tan-¹x, what is the slope of the tangent line to the curve y…

A: Here we have to find the slope of the tangent line.

Q: Solve the problem. A loaf of bread is removed from an oven at 350°F and cooled in a room whose…

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Q: Find the arc length of the following curve on the given interval. x=7t+1, y = 24t-7, 0≤t≤3 The…

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Q: Choose the normal vector of the tangent plane to the surface defined by at the point (-4, 2, e88). O…

A: Given problem:- Find the normal vector of the tangent plane to the surface defined by…

Q: Consider the following function. f(x) = (x - 3)ex (a) Find the critical numbers of f. (Enter your…

A: We have to find the critical points, monotone intervals and relative extremum.

Q: Solve the initial value problem y(t) = dy dt - y = 3e² + 18e¹t, y(0) = 9

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Q: Find the length and width of a rectangle that has an area of A square centimeters and a minimum…

A: We can find the correct answer by checking the individual options as below.

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A: Given that, the function is gx,y,z=xye8z and the points are P3,12,0 and Q0,0,0.…

Q: Let the function f(x) have the property that f'(x) = ¹.1f g(x) = f(x²) find g'(x). g'(x) = Solution:

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Q: Integrate I -dz Select one: O A In 1-¹-2²+√1 − x² + C I OB. 21n1-¹³+√1 − x² + C | OC. In 1-²+√1 = z²…

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Q: Solve this system of equations x2+2y=0 -y2+2x=0

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Q: The number of oil changes per hour at Quick Lube is described by the following short-term production…

A: answer is in next step .

Q: Sketch the region enclosed by y = 3x and Y = find the area of the region. 2x². Decide whether to…

A: Given that y=3x and y=2x2To find : Area between the region.Solution :

Q: In reference to the following function:  f (θ) = (θ − 3) cos(θ) Write down an expression,…

A: use the polar curve to find the expression of the area.

Q: 7. The critical points of the function f(x) = 1³-272 are (a) ±3 (b) ±1 (c) +√2 (d) 1

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use the Limit Comparison Test to determine convergence or divergence. O 8 Σ n=1 O Select the…

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Q: 1. The two graphs below (X & Y) show two functions from our library of common functions. For each…

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Q: The limit: exists, and equal to 0 Select one: True lim (x,y)-(0,0) Falas x-y x² + y² The gradient…

A: Here we have to check whether the statement is true or false.

Q: Use Newton's method to approximate a root of the equation 3x7 + 7x² + 2 = 0 as follows. Let 1 = 1 be…

A: Follow the procedure given below.

Q: The domain of the function f defined by is equal to: Select one: O True O False 7 cos(x)+y² In…

A: This question is based on logarithmic function.

Q: Evaluate the series or state that it diverges. Σ n=0 5-1 6n Select the correct choice below and, if…

A: To evaluate the series.

Q: the region enclosed by y = e¹¹, y = 5², and a e = 1. Find the area of the region.

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Q: The domain of f(r. y) = Select one True False 19-y V is the upper half of the disc centered at…

A: fx,y=9-x2-y2y

Q: Carbon-14 decays at a regular exponential rate. The half-life of carbon-14 is approximately 5730…

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Q: Use the formula for the general term (the nth term) of a geometric sequence to find the indicated…

A: For a geometric sequence with first term a1 and common ration r is given by an=a1rn-1, for…

Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations.…

A: We have to find area of given region.

Q: The temperature at the point (x, y) on a metal plate is T(x, y) = Find the direction of greatest…

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Q: if: z = cos 0+isin prove that: 1) 2+1 z+1 2)221 +1 = itan 0 z² = Z

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Q: 10 20 30 (a) Draw the tangent line at each labeled point. y 5 4 3 2 1 O y st 5 4 3 2 1 10 20 30 10…

A: Please see the below picture for detailed solution.

Q: Evaluate the indefinite integral. fest √5e³t sin (est)dt = [

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Q: Choose the gradient of the function f defined by f(x, y, z)= In[1 + (17xy + xz +9yz)²].…

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Q: Which of the following is a valid triple integral? ⒸSS ſo ſh(e) (5) f(x, y, z) dzdydr h(y,z) flus) f…

A: We have to discuss about valid triple integral.

Q: A spring requires 7 J to stretch from 1m to 4 m. An additional 4 J to stretch for 4 m to 7 m. What…

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