Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) =

Q: Solve the following items and show your solutions. a.) Find the general and particular solution of…

A: x dydx+2 y =4x2dydx+2x y =4xComparing with Bernouli's equation;y'+P(x) y = Q(x)P(x)=2x, Q(x)=4x

Q: sin 2x (1 - 2 cos 2x)? dx 6.

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Q: For what value(s) of z on [0, 7] is the value of f(z) = sin z +1a maximum?

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Q: Г(81)

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

Q: Find the centroid of the solid generated by revolving the region about the indicated axis the area…

A: There is more than 1 question, as per the Q&A guidelines, We are answering the 1st question. If…

Q: Determine whether the lines are parallel or identical. X - 5- y+ 4 z + 8 5 4 x + 7 = y - 5 z + 23…

A: The directional vector of L1:v1=4, -3, 5The directional vector of L2:v2:-8, 6, -10   : -2 4, -3, 5v2…

Q: What is the approximate value of x in the figure below?* 723 58 427 3244 ft. 3169 ft. 820 ft. O 3322…

A: Find your answer below

Q: *** . ***** ******* . Determine whether the lines intersect, and if so, find the point of…

A: To find the point of intersection of given lines.

Q: dx U x" Jx? +3 4

A: To find out the integration.

Q: (x² + y) dx – xydy = 0 O 2y = x In cx2 O y? = x? In cx? O O

A:

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

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Q: Recall: v = can be written as v = ai + bj + ck , where i = , j = and j: . Let v = – 2i + 5j – 4k…

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Q: Use the figures to calculate the left and right Riemann sums for f on the given interval and the…

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Q: Evaluate by separation of variables. dß %3D и(1 — и?) sec? р du 2 tan B+ sin 2ß = C – (1 – u?)? 2u?…

A: To solve the given differential equation.

Q: A function f(x) has a critical number x=c. Which of the following statements is always true about…

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Q: The Maclaurin series for f(x) = x²e=* is E-o(-1)" xn+2 п! False True

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

Q: What are the relative extrema of the function f(x)=x^3+3x^2-24x+7 a. relative minimum of -4,…

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Q: Select

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: Q1. Evaluate the integrals below using the integral rules derived in Lectures 13-15. For each…

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Q: e" + e¯ cosh(r) : e - e sinh(r) 2 Use our rules for differentiating e" to show that cosh'(r) =…

A:

Q: VECTOR DIFFERENTIATION: If R = e^(−t) i + ln(t^2+ 1) j - tant k. Find: (a) dR/dt, (b)…

A: R=e-ti+ln(t2+1) j-tant k

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: Evaluate by separation of variables. dB du = u(1 – u²) sec 3 O 2u? + sin 28 = C – (1 – u²)² O 2 sec…

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Q: Find the slope of the line passing through the points (-1, 3) and (-8, 3). slope: | Find the slope…

A: Solution ) slope  m = (y2 - y1)/( x2 - x1) 1) point ( -1 , 3 ) , ( -8 , 3 ) slope m = ( 3 - 3 )/( -…

Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

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Q: EVAUATE FL) OF TRE DIFF ERENTIAL EQUATION AT zEto NITI AL CONDITONE. oit

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Q: ) Given the following derivative function 2x – 5 f'(r) = Þ – I^ what are the critical numbers of…

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Q: Find the following limit by evaluating an appropriate definite integral over the interval [0, 1 lim…

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Q: A 400-lb cable is 250 feet long and hangs vertically from the top of a building. How much work is…

A: Work = Force × displacement

Q: Find the complex zeros of the following polynomial function. Write f in factored form. f(x) = x° -…

A: Here we have to factorize the given cubic equation.

Q: dy = 8x - 7 and y(9) = 0. dx Find the function y(x) satisfying

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Q: he power supply of a satellite is a radioisotope (radioactive substance). The power output P, in…

A: Given: The power supply of a satellite is a radioisotope radioactive substance. The power output P,…

Q: Evaluate ſV7– x²dx

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Q: -8e4t* + 2e6t cos 2t

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Q: Integrating Factor by Inspection: (1) y(x² + y² – 1)dx + x(x² + y² + 1)dy = 0

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Q: Solve the following items and show your solutions. b.) Identify if the following functions are…

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

Q: Use the position function s(t) --4.9+ 650, which gives the height (in meters) of an object that has…

A:

Q: After its fastest rate of growth ever during the 1980s and 1990s, the rate of growth of world…

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

Q: The table below shows the velocity of an object.(cm/sec) at each sec as it moves along a track for…

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Q: S4tan3 (пх + 1)dx

A: ∫ 4tan3πx+1dx=4·∫tan3πx+1dxLet u=πx+1.=4·∫tan3u1πdu=4·1π·∫tan3udu=4·1π·∫-1+sec2utanuduLet…

Q: Differentiate implicitly to find dy Then find the slope of the curve at the given point dx 8x-9y…

A: topic - implicit differentiation

Q: ds For the following function find the antiderivative s that satisfies the given condition. dt ds =…

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Q: Solve the initial value problem. d?r 2 dr = 5, r(1) = 4 dt2 dt t=3

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Q: Consider a right pyramid whose base is an equilateral triangle of side 4 cm each. If each slant edge…

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Q: Solve the system by graphing each equation and finding the point of intersection. -12 + 6 x + 2 y -…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 – 2xy + y²,…

A: Given: f(x,y)=x2-2xy+y2, (5,7,4).

Q: S e2x sin 2xdx

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Q: tan x dx sec x+4 cosx 5.

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Q: Evaluate the integral where D is the region bounded by y = x, y = 2, and r = 0. Hint: One order is…

A: We will solve this question by changing the order of Integration.