2. Differentiate the following: (a) y = x²z

Q: Which of the following is the critical point of the function f(x, y) = x²y = xy? - Select one: ○…

A: The given function is: fx,y=x2y-xy To calculate the critical point, we have to solve the equations…

Q: Use the Root Test to determine whether a converges, where a is as follows. n n n = 1 = ( ²² + ²)² n…

A: We will apply Root test

Q: y(x) = 4x²y" + y = 0, y(-1) = 6, y'(-1) = 3 , x < 0

A:

Q: 3. The differential equation dy = =X dx 1. will produce a family of quadratic functions. II. will…

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Q: What is the value of the integral Select one: O 64 O 16 O None of these O 32 08 CO 2rydydz?

A: Given:       ∫04∫x42xy dy dx      =∫04∫x42xy dy dx     Taking out constant        =∫042x∫x4ydydx…

Q: The cross product of two vectors u=(2, -3, 1) and v=(0, − 1, 2) is 5. O True O False

A: Here is the solution:

Q: Test the series for convergence or divergence. Select the correct answer. The series is convergent…

A:

Q: The function f(x, y) = 5 - 3x² + y² + 7y + x has: Select one: O A. None of the others B. One…

A: fx,y=5-3x2+y2+7y+x We have to find how many critical points this function has.

Q: 1. Find the gradient of the function f(x, y) = x² sin y.

A:

Q: A function fis defined by that is, its coefficients are a = 5 and ₁+1 = 9 for all n 20. Find an…

A: Let's find explicit formula of given function.

Q: The integral ſº, ſº₁ x – y dædy is equal to: Select one: 0 O2 O 4 O None of them O-2

A:

Q: Evaluate the iterated integral: I 7-x X -SS e dyda 8 7 2

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Q: Solve the given initial-value problem. dx dt x(t) = y(t) = = -11x - y dy = 25x - y dt x(1) = 0, y(1)…

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Q: Obtain an exponential function in the form f(t) = Aert. HINT [See Example 5.] f(t) is the value…

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Q: Let R be the region bounded by y = 2x, y = 2 and x = 0. Sketch the region R and evaluate the double…

A: Given: I=∫∫Rxy-1dA And  y=2x, y=2 and x=0   As we know that; ∬dA=∬dxdy or ∬dydx

Q: Find the derivative of the function f(z) = √2 O None of these. 37 Of(z) = √2z f(2)=

A: We will find the derivative.

Q: Solve the given initial-value problem. dx dt dy = 25x - y dt x(1) = 0, y(1) = 1 x(t) = 0 = -11x - y…

A:

Q: In a display, there are 20 toys in the first row, 23 toys in the second row, and so on in an…

A: topic- arithmetic sequence

Q: 1. Which of the following is the general solution of the differential equation Oy²=x² +C að

A: We will solve the differential equation.

Q: Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation…

A:

Q: A boat is being pulled toward a dock as shown in the figure to the right. If the rope is being…

A: Let X be the distance of boat from dock (which changes with time ) And y be the length of rope  (…

Q: How many critical points the following function has, f(x, y) = 4x² - 2xy + 2y³? Select one: 0 2 O 0…

A: The given function is: f(x,y)=4x2-2xy+2y3

Q: A box with an open top is to be constructed from a 4m x 3m rectangular metal sheet, by cutting out a…

A:

Q: 1. Find the critical points of the function f(x, y) = x² + 4xy. 2. Find the local maximum and…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Describe the region D enclosed by:y=2, y=2r+2 and y=-2x + 2 as a region of type II: Select one: O D=…

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Q: 2. Find the local maximum and minimum values and saddle points (if any) of the function f(x, y) = xy…

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Q: Let R be the region bounded by the curve y = 3√x and the line y = 3x. Then the double integral /…

A: Given problem:- Let R be the region bounded by the curve y = 3√x and the line y = 3x. Then the…

Q: Question correct for the series : Which of the following is Σ n=1 Select one: O equals 4. O None of…

A:

Q: Evaluate the integral 2-x 2 [²² 0 0 xdydx.

A: Solve the integral ∫02 ∫02-x x dy dx. Concept used; Power rule of integration; ∫xndx=xn+1n+1+c

Q: Test the series for convergence or divergence. Select the correct answer. The series is divergent…

A: Given problem :- ∑m=5∞5mlnm6 Test the given seires for convergent or divergent

Q: Consider the function f(x, y) = y ln x - x ln y - . a Find the directional derivative of f at the…

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Q: 1. Find the gradient of the function f(x, y) = x² sin y. 2. Find the rate of change of the function…

A: The given function is;  f(x,y)=x2 Siny.

Q: L4Q12. Write an explicit formula for the sequence: - 2, 2, 6, 10, ... A.an = - 2 + 4n B.an = - 6 +…

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Q: (b) Use Simpson's Rule with n = 10 to estimate the area of the surface obtained by ro the cosine…

A: I have solved b part as asked.

Q: Find (A) f'(x), (B) the partition numbers for f', and (C) the critical numbers of f. f(x)= x³ -…

A:

Q: Miguel purchased a $9,000 bond that was paying a 4.25% compounded semi-annually coupon rate and had…

A:

Q: Evaluate plti 5. S z² dz using the formula [2² dz = A 3

A: This question is related to definite integration, we will solve it using given information.

Q: Work Problem 2 [ Question 1 You must provide a clear and detailed solution. Given the region D in R2…

A:

Q: Find the graph of the polynomial function f(x) = -x3.

A: we write a table for x=-3 to x=3 and calculate the values of f(x) for all these values and plot the…

Q: S 2 1-a Select one: O True O False e²e³dydx = - (₁ e²d²) (²* eºdy) (² dx 2

A: Given :∫01∫21-xexeydydx=∫01exdx∫21-xeydy

Q: Solve the given initial-value problem. y(x) = y" - 81y = 9, y(0) = 1, y'(0) = 0

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Q: Consider a particle that moves through the force field F(x, y) = (y - x)i + xyj from the point (0,…

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Q: Give an example of a derivable function f (x) with f ′ (- 4) = - 1

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Q: 2 ƒ² ƒ² (x − 3y²) dydx = −12. - Select one: O True

A: ∫02∫12x-3y2dydx=∫02x-7dx=-12

Q: dy Solve the differential equation (x+1)+y=4e*, x>0. dx The solution is (Type an equation. HE

A:

Q: L3Q15. Find (g/f) (x), if f(x) = x2 – 4 and g(x) = x – 2. A.x2 – x – 2 B.1/(x + 2)

A:

Q: The double integral 0 Select one: True O False 2 √x has triangular region. f(x, y) dy dx

A: We can solve as follows

Q: Suppose that f(x) is a continuous function on the interval [-1, 3] with f( − 1) = − 3 and f(3) = 3.…

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Q: Suppose F(z) = g(f(z)) and f(2)= 3. f(2)=-3, g(3) = -1 and g (3)=-4. Find F(2).

A: Recall: Chain Rule  Let F(x)=g(f(x)) , then F'(x)=g'(f(x)) f'(x)

Q: Given the graph of ƒ' (x) below, where the Dom f (x) = (-∞, ∞). Find the interval(s) for which f"…

A: We have the graph of f'(x) and  we need to tell where f''(x) is &gt;0So, f''(x)&gt;0 when f'(x) is…