1. Find all relative extrema and saddle points of the functon Use econd Partials Test where appli cable (If answer does not exist ty pe flx.y)= x²+y* +6x-16y-8 relative minimum (x,y,z) = DNE ) 11 %3D

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A: We know, ∫dx1-x2=sin-1(x)

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A: Use eigen value concept

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A: Given F(x,y,z)=4sinx i+7cos(9x-10y) j+10z kTo find∇·(∇×F) first we need to find ∇×Fwe know that ∇×F…

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A:

Q: Find the root of x4-x-10 = 0 approximately upto 5 iterations using Bisection Method. Let a = 1.5 and…

A: The root of x4-x-10=0 between a=1.5 and b=2

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A: Find div F and curl F

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Q: 2.) S- e2x dx ex – 5

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Q: In an extensive study of cost functions for 40 firms in Great Britain, it was found that if a is the…

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Q: 5. By Chain Rule , evaluate a. y' for y = u? + 4u and u = 4x3

A: This question is related to Differentiation, We will solve it using given information.

Q: ermine the Interval(s) for which the function is (a) increasing, (b) decreasing, and (c) constant.…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) COS X dx (sin x)20

A: Given, ∫cosxsinx20dx We have to evaluate the indefinite integral.

Q: 3. y = In? (csc2x). Find y"

A: y=ln2(csc2x)

Q: No new data to save

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Q: A force of 9 lb is required to hold a spring stretched 6 in. beyond its natural length. How much…

A:

Q: Find V. (F x G), if F(x, y, z) = 10ci +j+13yk and G(x, y, z) = xi + yj – zk. V. (F × G) :

A: To solve the following problem

Q: 1

A:

Q: Find curl (7z i + 8x j+4y k).

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Q: A balloon is rising vertically over a point A on the ground at the rate of 15 feet per second. A…

A: Let's draw the diagram first Given: dhdt = 15 ft/sec We have to find the value of dydt when h=40

Q: メーャゴ+2x)dメ+でyalyo

A: answer is in next step .please give a like

Q: Use the formula k(t) |r(t) × r"(t)|| x r" (t)|| to find «(t). ||r(t)||° r(t) = ti+ t5j «(t)

A: To find k(t).

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A:

Q: Evaluate: /1/T 1–x*dx (A 4) ² +c B D E) None

A:

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A: Find your answer below

Q: 2. A turns 100 RPM and B 150 RPM as shown; they are connected by rolling cones. Calculate the cone…

A: Solution: wa = 100 rpm wb = 150 rpm

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Q: 5. By Chain Rule , evaluate b. y' for y = u² + 2u and u = x² + 2 %3D

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Q: Find y': %3D Oy =- Oy=--

A: A detailed solution is given below

Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it converges…

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Q: 5. [sin-' x dx Ans. x sin'x - V1-x² +

A: We will use integral by parts to evaluate integration of arc sinx

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A: We will solve the given differential equations with condition

Q: 3. If g(x) = -dt, find g'(2). %3D

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Q: (a) / Which of the following integrals is equal to -2+ In 2? X - 4 dx (a) 4- I dx (b) 2 - 4 da (c),…

A: To find which of the given integrals has given value

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Q: dx x² + 4

A: A detailed solution is given below.

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A: We have to find the integral.

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Q: Evaluate the line integral / (2x + 4y)dx + (2x – 9y)dy along the curve C : x = 4 cos t, y = 8 sin t…

A: Solution is given below:

Q: Two numbers have a sum of 72. What is their product if it is a maximum? (A) 1296 B) 1297 c) 1298…

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Q: Sketch the region enclosed by y 6x and 4x. Find the area of the region.

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Q: Find r'(t). r(t) = (arcsin(t), arccos(t), 0) r'(t) =

A: This question is based on diffrentiation.

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A: