7. Use the Method of Lagrange Multipliers to find the extrema value of a function f(x, y, z) = 2x² + y² + 3z² subject to the constraint 2x - 3y - 4z = 49.

Q: Use geometry (not Riemann sums) to evaluate the following definite integral. Sketch a graph of the…

A: This question can be solved using the concept of geometry to solve definite integrals.

Q: al speed seball, hit 3 feet above the ground, leaves the bat at an angle of 45° and is caught by an…

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Q: Solve the given initial-value problem. y(x) = y" + 6y' - 7y = 11e2x, y(0) = 1, y'(0) = 1 2x -7.x 7e…

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Q: Find the limit. lim (x,y) → (5, 1) ety Discuss the continuity of the function. O continuous…

A: See this solution in below

Q: Compute u v if u and v are unit vectors and the angle between them is R|4

A: we know that u.v =uvcosθfor unit vector u=v=1given θ=π4

Q: Complete the following steps for the given function, interval, and value of n. a. Sketch the graph…

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Q: (B): Find the tangent equation to the curve y = sin² x at point x =

A: I have stated the used formulas in the solution.

Q: Find the length of the following three-dimensional curv r(t) = (9+5t,3-2t,-1+2t), for 1sts6

A: To find the length of the given three dimensional curve.

Q: 1-). 25 2-) 3+4i 3-1

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Q: (B): If A = 2i + 3j - 4k; B = 3i - 4j + 5k and C = i + j - k, find: (ii)B.C (iii)A. (B+C)and (A+B).C…

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Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

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Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(0) and y = r sin(0), and note that (x,…

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Q: Use the graph below to answer the following questions. f(c) -6 -4 5 14- 12 10- 8 6- 4 2- 2 -4- -6-…

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Q: (g) Determine the minimum or maximum value of the function. (h) Write the domain and range in…

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Q: cise (a) e volume of the solid formed by revolving the region about the x-axis 01 he region is…

A: To find the volume of solid revolving around x axis using disk method

Q: (B): Find the unit vector perpendicular to the vectors: 31-4/+5k 41 +5/-6k i (C): If w = tan x and…

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Q: 2. y(x4-y²)dx + x(x++y²)dy = 0

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Q: Use the figure below to find the exact value of the trigonometric function of angle A. sin (A) 6 A…

A: it is very basic question of trigonometry.

Q: 6 ∞ 9 cos (7) x² dx I

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Q: 818 B. Find the horizontal, vertical, and oblique asymptotes of the curve y =

A: In this question, we want to find the vertical, horizontal and oblique asymptote of the given curve.…

Q: Q1: Fill in the blanks for the following statements (chose five only) 4n 1. lim-00 2n+1 2. log10 (3x…

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Q: Find the solution to the initial value problem. dy = 2√√√√t, y(1) = 7 dt y(t) =

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Q: 3. Solve one of the following inequalities. Write your answer as an interval or union of intervals.…

A: This question is based on finding solution of inequality.

Q: prove that :: 2) (1+i) (1-1)² = 64

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Q: 013 Verify that the function satisfies the two hypotheses of Mean Value Theorem on the given…

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Q: 7. f* (x² + 8) & dx CO (³ (x-1)

A: We have to solve integral

Q: 0²1' (19²¹) = (1) 1

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Q: -2- 0 y = g(x) 4 7 x

A: To evaluate the integral.

Q: Q1/ Solve the following differential Equations. 3- dx +2²= 3x x

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Q: Sketch the space curve. Function r(t) = (5 sin t, 3t, 5 cos t) 1.0 0.5 0.0 0.0 -0.5 -1.0 -5 N 0.5…

A: Please see the below picture for detailed solution.

Q: A. Find the following limits. Answer four only. x-¹-1 i. ii. iii. lim- X-1 X-1 lim 4x-x² X-4 2-√√x…

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Q: 1. Find the total area bounded by the curves y=x²-3x and y = x³ + x² −12x.

A: Given Graphs y=x2-3xy=x3+x2-12x First we find point of intersection of graphs…

Q: Given the equation 5 sin 6xy = 3, evaluate dy Assume that the equation implicitly defines y as a…

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Q: Why do you do e to the power of the integral in order to solve the question? Why not just integrate…

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Q: 04: Answer two only: (A): I A-2 1 -1 1-2 Find AB and AC.. -- 3 1 1 and 1 3 1 CO

A: Given :A=420210-2-11, B2312-2-2-121, C=31-3026-121

Q: 3. (x³+xy²-y)dx + (y³+x²y+x)dy =0

A: We need to find the solution for (x3+xy2-y)dx+(y3+x2y+x)dy=0

Q: 2: io ue Approximate the area of the region bounded by the graph of f(t) = cos (t/2-5/8) and the…

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Q: Find the critical points of the given function. a) f(x) = 2/3+¹/3+x−2/3

A: Since multiple questions are asked, I am answering first question

Q: 12. x² sin(x + y) = 1, -

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Q: For f(x) = 6x and g(x)=x+8, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(2); d.…

A: Solution ) f(x) = 6x , g(x) = x + 8  a) (f o g) ( x ) = f ( g(x) ) = f( x + 8 )  = 6 ( x + 8 )  = 6x…

Q: dy Q5: Find for the following functions: dx (3) y = et sin²x In√x

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Q: the displacement is correct, but the distance is wrong

A: The velocity function is v(t)=-t2+6t-8 on the interval -3,5

Q: The amount of a radioactive substance, y, decays exponentially such that its half-life is 8 days. In…

A: topic- differential equations

Q: Q2: Solve the following integrals: (1) f 7x²+14x+15 (x²+3)(x+7) dx ; (2) S sin x+cos x sin³ x cos³ x…

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Q: A spherical raindrop evaporates at a rate proportional to its surface area with (positive) constant…

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Q: A solid of revolution is formed by revolving about the x- axis the region bounded by the curve y √2x…

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Q: Q2: Solve the following integrals: (1) f 7x²+14x+15 (x²+3)(x+7) 02 dx ; u nein!! sin x+cos x (2) […

A: We have to calculate the given indefinite integral according to the given information

Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

A: Find determinant of coefficient Matrix  Then find delta x ,delta y, delta z

Q: -1 t² Vta 6 dt

A:

Q: Find the indicated limit by using the limits 6f(x, y) lim (x,y) → (a, b) g(x, y) lim (x,y) → (a, b)…

A: Given: lim(x,y)→(a,b)f(x,y)=3lim(x,y)→(a,b)g(x,y)=-5To find:lim(x,y)→(a,b)6f(x,y)g(x,y)