I. Find əx and and (whenever possible) for the following functions. az ne ду 1) w%3D 5x*у — 11ху3 + 7ху— 8х 5x*у — 11ху3 + 7ху — 8х 2) w %3D 2yTan(2х + у) — ЗxSec(х?у3)

Q: 1. a. Show that two lines with direction vectors d (2,3) and d, (6,-4) are perpendicular %3D b. Give…

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Q: Find the Taylor polynomial of order 3 generated by f at a. f(x) = x2 + x+ 1, a= 7

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Q: t2, -8 + 3t, g(t) = l(t -6)* + 2 cos (: -). – 6)? + 2 cos (-),

A: answer is in next step

Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ +…

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Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.…

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Q: 6. ( alv.y s. Match each of the following formulas with the given graphs. Justify your answers as…

A: We have to match functions with the graph

Q: 1. Find the equation of the plane containing the lines L1 and L2 given below: z = 4t + 3 z = -4s – 1…

A: Given :L1:  x=2t+1, y=3t+2, z=4t+3L2 : x=s+2, y=2s+4, z=-4s-1

Q: Find p1 and p2, the prices per unit (in dollars), so as to maximize the total revenue R = X1P1 +…

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Q: 9. Determine the points of inflection and discuss the concavity of the graph of f (x) = x* – 4x²

A: Given : f(x) = x⁴ - 4x²    -----(i) We have to find point of inflection and the concavity of the…

Q: The rectangular coordinates of a point are given. Plot the point. (-3/7, -3/2) -6 -4 -2 6 -6 -4 -2 4…

A: Given query is to plot the point and find the polar coordinates.

Q: ind the values of a and b so that the function = x + ax + b has a local maximum at the (-16,- 12).

A: We will find the value of a and b.

Q: Using the Laplace transform to solve the IVP: y" - 4y = 4, y(0) = 0, y'(0) = 0 we get 4 Y(s) = s(s?…

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Q: Sketch the region enclosed by ?=5?y=5x and ?=3?2y=3x2. Decide whether to integrate with respect to…

A: Given: y=5x, y=3x^2

Q: Evaluate the definite integral using integration by parts. Do not use any other met od. You must…

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Q: Given the differential equation dy dx (x – 1)(x + 2)' x +1 y = 1- y > 1, x> -1. a) Find the solution…

A: Here we have given a linearly differential equation :

Q: dx x3+27 8. Evaluate

A: We have to find the integral

Q: Find the slope of the tangent line to the r=2-3cos 0 in polar coordinate at 0 =

A: Given:-r=2-3cosθdrdθ=3sinθTo convert from Polar Coordinates (r,θ) to Cartesian Coordinates (x,y)…

Q: Consider the points A(2, –1,3), B(7,0,5) and C(0, 1, 7), and the line l with symmetric equation x –…

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Q: 2. All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface…

A: topic- application of derivatives

Q: h(x) = (2x2 - 5x)2 / √3x-2 1. Explain how the function you chose can be rewritten in such a way…

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Q: Find the volume of the solid generated by revolving the area bounded by the given curves about…

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Q: x = -2t Given: line l1 : 3 1 – y = Z - 8 and l2 y = 2 + 2t z = 6 + 2t %3D 1. If the given lines…

A: The solution is given in the next step.

Q: DEFINITION

A: We will find the Laplaces Transform.

Q: Find all the second order partial derivatives of the given function. f(xy) =xy° +y¢* +5 O A. f = 2x,…

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Q: a spherical balloon is filled with gas at a rate of 300 mm3/sec. Find the rate at which the surface…

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Q: Explain, using the theorems, why the function is continuous at every number in its domain. 2x2 – x –…

A: 2x2-x-4x2+9  Function fx is continuous on interval a, b if it is continuous at every point. We know…

Q: (3) 2x Find the linearization L(x,y) of the function f(x,y)= e cos (3y) at the points (0,0) and 0,…

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Q: ley'z ds, Cis the line segment from (3, 1, 2) to (1, 2, 5)

A: Given ∫c y2z ds Where c is the line segment from (3,1,2) to (1,2,5) Parameterize the line  r(t) =…

Q: parhod derivohve of 4,5 43 6- 13

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Q: dw I. Find dw and and ду aw (whenever possible) for the following functions. - - dz 1) w = 5x*y –…

A: Let's find.

Q: Given the points A(-2, 3, 1), B(0, 0, 2), and C(-1, 5, -2) Determine ZBAC, the angle between AB and…

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Q: Guen F(x)= 4sin? (x), write the equaton ok the live tanjut to y=F(x). when x= 7r %3D 4.

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Q: 5x - 4 and the a-axis over the interval 6 Find the net signed area between the graph of the function…

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Q: Calculate the trapezoid approximation of o xdx using four subintervals. O T5 = 21.52 O T5 - 23.25 T5…

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Q: What is the surface area of the solid generated by revolving about the y-axis, y =1- a2, on the…

A: Surface Area of the solid generated by revolving about the y-axis ,S = ∫x=ax=b 2πx 1+dydx2 dx

Q: Given the slope field below, which function describes the given graph. A. y' = x? + y +1 B. y' = x*…

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Q: Differentiate the following using implicit differentiation 3/a + V =7

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Q: (D³ - 7D + 6)y = 0 %3D

A: Differential equation

Q: 2) lim- x) Tanx

A: The given limit is              limx→π2π2-xTanx we know,     Tanx= sinxcosx

Q: 4x Find the linearization L(x,y) of the function f(x,y) = e cos (3y) at the points (0,0) and0,

A: Answer is given below

Q: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 6 Po(x) =

A: nth Maclaurin polynomial for the function f(x) :       Pn(x) = f(0)+f'(0)x +f''(0)…

Q: Jk, when = & Case y: 2 Sing

A: Solution 1:

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

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Q: By considering different paths of approach, show that the function below has no limit as…

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Q: 1. The graph of function f(x) is shown below. y f(x) (a) By using the graph of f, explain how we…

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Q: (e) If p = tą+3ī , then p, q, andr must be coplanar F Ccould be wltihear)

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Q: Tangent to the curve z2 = 2xy + x² , z = 3 , at the point ( 1, 4 , 3

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Q: 5x(x+1) =15

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Q: Two lines have equations L1: (0,0,1) + s(1,-1,1), s e R and L,: (2,1,3) + (2, 1,0), e R. 10. What is…

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Q: Find the curvature of the curve 7(t) = (3 cos(t), 3 sin(t), 3t) at the point t %3D Give your answer…

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