Encounter the critical points of f(x, y) = 16x3 - 9y2 - 36x2 - 12y + 6x - 27 and then denote each point's nature with the second derivative test.

Q: Describe all absolute extreme points of P. Select the correct choice below and, if necessary, fill…

A: Let's find.

Q: dx -4x-7

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Q: Show that - 8. ==1+* +4++++1=

A: We know ∑1n2=π26  Hence, ∑1(2n)2+∑1(2n+1)2=π26 Therefore, 14∑1n2+∑1(2n+1)2=π26 ∑1(2n+1)2=π26 - π224…

Q: Jse the linear approximation to estimate AS = f(3.1) – f(3) for f(x) = T Use decimal notation. Give…

A: Here, the given function is: f(x)=31+x2⇒f'(x)=3-1(1+x2)2(2x)=-6x(1+x2)2

Q: _5. Given the fox²dx, which of the following is the integrand? A. O B. 2 C. x D. dx

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Q: 2. Evaluate the given line integral, (-y, x – y) · dR, where C is the line segment from (2,0) to (0,…

A: Using parametric equation, line integration is evaluated.

Q: The approximate value of -31.8 using linear approximation, O -1.0075 O -2.0025 O -1.9975 O (E) None…

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Q: sove the focowing using Lagrange Multiptiers: Maximi ze flx, Y, 2) solaject to x2 + y + 22 =1 Ax +…

A: Method of Lagrange Multipliers : 1.) Solve the system of equations .…

Q: 2en cos 2t s+ 2 Option 2 None of the choices 2s s2 -2 s2 -2 O Option 5 Option 3 2s s2 +4

A: Given :2eln cos2t

Q: Line 1: 3 1 — у - = Z – 8 2 - 4 Line 2: X=-2t y=2+2t z=6+2t 1.If the given lines intersect at a…

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Q: 2) lim- x) Tanx

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

Q: tan () (9) sin (4) F. Evaluate the integral r2 cos ()

A: integration

Q: Use differentials to find the approximate value of y: (2x – 1)* when x = 0.98. O (E) None of the…

A: Given :f(x)=2x-14x=0.98

Q: sin 2t sin 5t 20 s4 + 58s² + 441 None of the choices Option 3 10 1 s4 – 58s² + 441 2 s2 + 32 s2 + 7?…

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Q: 3s – 14 - s2 – 4s + 8 - 3e2t cos 2t + 4e" sin2t 3et cos 2t – 4eª sin2t Option 1 Option 2 4e" cos 2t…

A: Given: Fs=3s-14s2-4s+8   As we know that; The inverse Laplace transform identity. 1).…

Q: x = -2t x - 3 1 – y Given: line l1 : 4 = % – 8 and l2 2 y = 2+ 2t - % = 6 + 2t 1. If the given lines…

A: We have to find angle between the lines L1 & L2

Q: Use differentials to estimate the relative error in the lateral surface area of a right circular…

A: To find out the relative error in the lateral surface area of the cylinder.

Q: Solve the given initial-value problem y' + (tan.x)y = cos²x, y(0) = -1

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Q: -dx x2 +9 I x3 +ar-23 ton- (특) +C a. 3 b. 1 x³ t qx + 27 tam " ) + C b*3-9*+27€an )+c C. d.늘-9x- 2구…

A: Using substitution method, integration is done.

Q: a²z For each of the following functions z, find a²z a²z and ду? дх2 дудх' дхду 2. z= sin3x cos4y

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Q: Evaluate the following integrals using Trigonometric Substitution: 1. X-1- 16x dx

A: integration using substitution

Q: Use the Linear Approximation to estimate Af for f(x) = , when a = 2 and Ax = 5+x2 (Use decimal…

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Q: A plane P, in R'is perpendicular to the vector i = (4, 5, 7), and contains the point (3, 3, 8). a.…

A: A plane P1 in R3 is perpendicular to the vector n→=4,  5, 7, and contains the point 3, 3,  8.a To…

Q: (6) Use the linear approximation of the following (Answers are to be expressed in 4 decimal places.)…

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Q: xチ+1=4 DIDX= 2-2y (ost) X= 3サ-3 *キーに h で3,0) サ=2メー オー×ポーカ toノー4) メッとナ+ム メーリー3

A: Explanation of the answer is as follows

Q: II. A particle is moving along a line with velocity given by the function v(t) = t-…

A: We have to find the position function of the particle at any time t.

Q: If the tangent line to y f(x) at the point (1,2), passes through the point (-1,1), then f'(1) = %3D…

A: Find f'(1)

Q: 5. A Ferris wheel has a radius of 20m and takes 2.5 minutes to rotate once. a) How far does a rider…

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

A: We have to solve above problem.

Q: 1. Given the vector ū = (2,0, 1). (a) Solve for the value of a so that ữ and i = (a, 2, a) form a…

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Q: Give the symmetric equations of the line l perpendicular to the plane T : 5x – 2y = z+4 and passing…

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Q: 3 4 11) –3 0 -5 Ans. r = 2 - 4 5

A: A detailed solution is given below.

Q: Question 1 Determine the inverse Laplace transforms of: 2s2-5s-1 (a) (s+3)(s²+9)

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Q: 100 dx 4.

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Q: 4. A car costs Php 800,000. Find its value after 4 years if it depreciates 20% of its cost per year.

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Q: Use Method of Variation of Parameters: [D² - 8D + 16]y = e4Xsec2x %3D

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Q: Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 5+x2 (Use decimal…

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Q: II. Let f(x, y, z) = z° sin a + Determine 2 dydzərəz'

A: We know, ∂2f∂y∂x=∂∂y∂f∂x

Q: y" + 4y= cos'x

A: Given: y"+4y=cos2x

Q: 4. Consider the curve with equation y = x* as shown in the diagram. A tangent line meets the curve…

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Q: Compute the area enclosed by the curves. You must show your work. Express your answer as a fraction.…

A: In this question we have to find the area enclosed by the curves.

Q: 6. The radius of a sphere is measured to be 7 cm, with a possible error of + (1/10) cm. Estimate the…

A: Volume of sphere   V=3π​r3/4 Percentage error in volume    ΔV​×100/V=3×Δr​×100/r =3*1*100/10*7= 4.3…

Q: Question 1 Determine the inverse Laplace transforms of: 2s2-5s-1 (a) (s+3)(s²+9) (b) 352+5s+1 (d)…

A: Let's find.

Q: Find the Laplace Transform of the functions 1. e-2t (cos t + 3 sin t)

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: (D³ - 3D² - D + 3)y = 0

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Q: ²+² +1) d + a (a – 2y) dy = 0 %3D

A: Given problem:- Find the solution of the given differential equation:  (x² + y² + 1) dx + x (x - 2y)…

Q: Question 1 Compute v31.6 approximately by use of differentials. O 1.995 O (E) None of the choices O…

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Q: I. True or False: Write True if the statement is always correct, otherwise write False. 1. All…

A: Topic:- function  Note:- as per our guideline if more than three subparts posted than only first…

Q: A man of height 1.7 meters walks away from a 5-meter lamppost at a speed of 1.5 m/s. Find the rate…

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Q: 1-x2 So Si S dz dy dx 0. 0.

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