Use Lagrange multipliers to find the maximum and minimum values of ƒ subject to the given constraint. Also, find the points at which these extreme values occur. f(x, y, z) = 39x + 12y – 56z; x² + y² + z² = 19204 NOTE: Enter the exact answer. Maximum : at (?, ?, ?) Minimum : at (?,?, ?)

Q: Find the centroid of the region. NOTE: Enter the exact answers. (ë, g) = | (?,?) y = z

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Q: 3. dy Find if y 2xy - x: dx = cos X using implicit differentiat

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A: Given;  v(t)=t2-t-12.

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A: Unit tangent and normal vector

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A: Given : y=3x-5 ,   -2≤x≤3   To Find : Arc length

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A: We have to find area of shaded Region.

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A: We have to find the volume of the solid.

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Q: h sin 2 xdx X COs 2

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Q: Find the area of the region inside the circle r = 12sinθ and outside the cardioid r = 4 + 4 sinθ.

A: Area

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Q: Find the divergence of the vector field F. F(x, y, 2) = In(9x+ 8y² )i + 72xyj + In(8y² + 5z? )k #6…

A: Solution is done in step 2 and 3

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Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

A: Given

Q: Find the exact arc length of the curve over the stated interval. y = 8x2/3, from x = 1 to x = 8…

A: The expression for the arc length of the curve is: L=∫x1x21+dydx2dx   Given; y=8x23x1=1 &amp; x2=8

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. V64-22 xy dy dx dz

A: Given: I=∫08∫064-z2∫0xxydydxdz   The Power rule: ∫xndx=xn+1n+1+C

Q: 32. If y=x^(3/2) what is the approximate change in y when x changes from 9 to 9.01? a. 0.045 b.…

A: Topic:- Basic maths  Note :- as per our guideline if more than one question uploaded than only first…

Q: Find the area of the region bounded by the graphs of f (x) = x° and g (x) = x. (А) 1 B c) 0.5 D 3

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Q: 2. Write the given (total) area as an integral! a. The area above the x - axis and below y = 4 -x2 T…

A: Area between the curve  y=f(x) and x-axis is defined as ∫abf(x)dx where a, b are point of the…

Q: Consider the following planes. 3x + 4y – z - 56 x - 8y + 2z = 0 (a) Find the angle between the two…

A: Find the angle between the two planes..

Q: find the equation for x in y=3x-x^3

A: Solving

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Q: Perform the indicated operation. Simplify if possible. b2 64 b+8 b+8

A: To simplify the given expression.

Q: for the given path. C: x = 2 cos(8), y = sin(@), o se s 27

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Q: Determine the area of the region enclosed by y3x^2 and y=x^1/2

A: To find the area of the region enclosed by the given curves.

Q: For neN simplty 2-글 + 4-1 +8-금+16-습+. + +2"-그 2n

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Q: Find the area of the region outside the cardioid r = 4 – 4 cos 0 and inside the circle r = 8. NOTE:…

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Q: test the converg ence and divergence 27-1 2. (2h-1):

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim t+o 5t2 + 6't (?,?) - (

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Q: Find div F and curl F if F(x, y, z) = x°i – 9j + yzk. - div F= curl F=

A: Divergence of a vector function F(x,y,z) is given by, div(F)=i∂∂x+j∂∂y+k∂∂zF and curl of vector…

Q: Evaluate (2x – y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (8, -5) Need…

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Q: Evaluate the definite integral. i+e"j+tk)dt (e^ – 1) i – (e- - 1) j+ k O e - i+ (e" - 1) j + k 1 O…

A: A detailed solution is given below

Q: 1. Find the equation of the tangent line to the curve x = e', y = et at t = 1.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1.

A: The given integral is ∫c(x+3y2)dy   and the curve C is x=2t,  y= 6t   where 0≤t≤1 Now, y=6t⇒dy =…

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: We have to calculate volume of solid obtained by revolving the region enclosed by curves x=cosecy,…

Q: 11 Evaluate the iterated integral. JJ, J, (x² + y² + z?) dx dy dz A 5 в) з D 10 00

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Q: Find the area of the region bounded by the equations y= x and Y3D6X-x². Note: theses are conics.

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Q: Use the arc length formula to find the length of the curve y = 3x – 5, -2sxs 3. Check your answer by…

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Q: Question 10 2 c y? Evaluate the iterated integral. J. yz dx dz dy -1 A 45 В) 34 © 47/3 D 5

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Q: Find the inverse of the function. f(x) = 9-2x^3 f^-1(x) =

A: THIS QUESTION CAN BE SOLVED USING THE CONCEPT OF INVERSE OF FUNCTION.

Q: Find the approximate area under the curve of f (x) = x< +1 from x = 0 to x = 2, using 4…

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Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: We need to evaluate integral using Green's theorem.

Q: Verify Green's Theorem by evaluating both integrals ам | y2 dx + x2 dy dA ду for the given path. C:…

A: Solution is given below: