Find the volume of the solid that lies under the surface z = 3y²x²+2 and above the rectangle R = {(x,y) : −1≤ x ≤ 2,0 ≤ y ≤ 3}.

Q: Suppose f(x) = 19x + 18e. Find: f'(2) = =

A: To find f'(2)

Q: Find and classify the intersection of the line = (5,−5,2) + t(2,−5,3) and the plane 9x + 13y - 2z-29…

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Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = 8y sin (2x)

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Q: 583 What is the area of the region bounded by the graph of the polar curve r = A B D 7T 9 14m 9 2 1+…

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Q: 35. y" - 2y"+y' = 2 - 24e* +40e³x, y(0) = 1, y'(0)=, y"(0) = −²

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Q: You invest $2,540 at a rate of 7.8% with continuous compounding. How much will you have after 7…

A: invest amount is $2540rate is 7.8%time=7 years formula for compound continuous is A=Pertwhere A is…

Q: Find a unit normal vector for the following function at the point P(5, -2, 125): f(x, y) (Please…

A: Here we have to find the normal vector.

Q: 2. T S and S the Second. R •P Assume that circles T, and T₂ intersect at right angles (i.e., that…

A: Let O be the center of circle gamma_1 and P be the center of circle gamma_2. Let Q be the point of…

Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. S…

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Q: is conservative. a= F(x, y) = 2.x (3.y + 1)i + a.x²j Next find a scalar potential for the vector…

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Q: Let f'(x) = f(x)= x cos ³

A: The given function fx=xcosx3. We have to find its derivative.

Q: The partial fraction decomposition of where f(x) = g(x) = h(x) = x² +23 c3+5x2 can be written in the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 91. A model for the surface area of a human body is given by the function S = f(w, h) =…

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Q: Get T, N, and kappa for the spatial curves of the exercises. 9. r(t) (3 sent)i + (3 cost)j + 4rk 11.…

A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…

Q: Find the maximum of f(x,y) = 3y2 + 5xy - 3x2

A: According to question,Given Function,f(x,y) = 3y2 + 5xy - 3x2

Q: Find the derivative of the function at Po in the direction of A. 0 f(x,y,z)= -3ex cos (yz),…

A: Solution will be given below   i+3j+2k is written as (1,3,2) [ In the vector form ]

Q: Compute 1 (x² + 1)(x² + 4) Lo -dx.

A: Given ∫-∞∞1( x2 + 1 )( x2 + 4 )dx

Q: Let z=x²y, where x(s,t) and y(s,t) are differentiable functions with values Әx Əs x(2,0) = 4, y(2,0)…

A: Given : z = x^2.y

Q: [2-R] [CLO 9] The set of solutions to the equation (x − 9)² + (y − 3)² = 49 is a circle in the…

A: Given query is to find radius and centre of the circle.

Q: Given s(t)=4t+16t, find (a) v(t). (b) a(t). (c) the velocity and acceleration when t = 2. (a) v(t) =…

A: Given: s(t)=4t2+16t   Concept: The instantaneous velocity at a given time is the derivative of a…

Q: A patient is adminstered a dose of 60 mg of a drug. If the body naturally disposes of 3​% of the…

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Q: UPVOTE WILL BE GIVEN. PLEASE WRITE THE COMPLETE SOLUTIONS LEGIBLY. SOLVE IN 2 DECIMAL PLACES. BOX…

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Q: Find y' and y". y = cos(x²) y' -sin(x²).2x ✓ = y" =

A:

Q: A company produces computers. The demand equation for this computer is given by p(q)=−5q+6000. If…

A: According to question,Given demand equation,p(q)=−5q+6000.

Q: Use the price-demand equation below to find E(p), the elasticity of demand. x = f(p) = 17,500 - 325p…

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Q: 25. N= ƏN ди 7 p+q p+r ƏN до p = u + vw, q = v + uw, r = w + uo; ƏN 2, v = 3, w = 4 дw when u =

A: We have to find partial derivative. “Since you have posted multiple questions, we will provide the…

Q: -. Solve the following differential equations 1) 2) d²y dx² d²y dx² dy +4² +4y=x²²e-²x, dx dy 6…

A: Given that a second order differential equation and we find this solution.     Here i attached the…

Q: A campus student group is raising funds for charity by selling cups of boba tea. The expenses…

A: A campus student group is raising funds for charity by selling cups of boba tea. The expenses…

Q: high school is organizing a dinner event for alumni. The planning committee has decided to rent a…

A: To write down the function for the amount that each attendees pay,

Q: Consider the indefinite integral Then the integrand decomposes into the form с d ax + b + where a =…

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Q: Given that lim f(x) = 9 X→ 1 (b) find the limits, if they exist. (If an answer does not exist, enter…

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Q: the answer on my test corrections is showing 2 with margin:0, could you explain more?

A: To evaluate the following limit. limx→0 sin6xx2+3x

Q: A company purchases a blueprint plotter for $1500. The plotter cost for each set of blueprints is…

A: Let's assume that the total cost of producing 'x' sets of blueprints is C(x), where C(x) is a…

Q: If √√x + √y=9 and y(16) = 25, find y'(16) by implicit differentiation. y'(16) =

A: x+y=9given  y(16)=25d dx(xn)=nxn-1d dx(constnat)=0d dx(x)=12x

Q: 45. S sin x sin 2x dx

A: SOLUTION: Question-45: Given that ∫sinxsin2xdx.......(1)  Now we know that…

Q: 8. If it [13,7.-2] is orthogonal to v v=[-5, k.7], determine the value(s) of k.

A: Given query is to find the value of k.n

Q: 8. Select the inverse of f(x) = ½¼½ (2)* + 1. [ƒ¹(x) = log₂ (2x + 2) |_ƒ^¹ (x) = log₂ (1/x -…

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Q: an+1 n→∞ an Let (an)1 be a sequence with positive terms, such that lim [Hints: = = 2023. Show that…

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Q: The graph of the derivative f' of a function f is shown. y 0 2 X = y = f'(x) 4 6 X (a) on what…

A: If the part of the graph is on or above x axis then y≥0.   If the part of the graph is on or below x…

Q: the right triangle shown, explain why v = (π/2) - u. Explain how you can obtain all six cofunction…

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Q: b. y = 4x (2x-1)⁹

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Q: Suppose f(x) = 7x²+5x. Find: ƒ'(1) =

A: Given: f(x) = 7x2+5x

Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(-4, 5, -11) for the function…

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Q: Find and sketch the level curves f(x,y) = c on the same set of coordinate axes for the given values…

A: Please see the explanation below

Q: S sech tan¹3x tanh tan ¹3x dx 1+9x²

A:

Q: A patient is adminstered a dose of 60 mg of a drug. If the body naturally disposes of 5​% of the…

A: Given: A0 = 60 Dispose rate (k): 5% = 5/100 = 0.05 Amount of drug be changed after 7 years T = 7

Q: 8) Expand the following binomial expression: (x² - 3)4.

A: o expand the binomial expression (x² - 3)^4, we can use the binomial theorem which states that: (a +…

Q: sum of an infinite series is given by S= 25/(1+3/4) What is the common ratio of this series? A. 25…

A: Given query is to find common ratio.

Q: Find the maximum rate of change of the function f(x, y) = = 4y+ X at the point (3,5)

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Q: Consider the weighted inner product defined by or functions f and g. (f,g) = [¹ f(x) g(x) dx, The…

A: To define the function inner_product(f, g), we can use the integral function to compute the…