Evaluate the definite integral. NOTE: Enter the exact answer. 8j i2 + 3

Q: Find the first partial derivatives with respect to x, y and z f(x. y.2) - 3x°y - 9 xyz + 10 yz² %3D

A: Given

Q: Find V x (V × F) if F(x, y, z) = 5xyj+ 10xyz k. V × (V × F) =

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Q: A man 6 ft tall is walking toward a building at the rate of 5 ft/s. There is a light on the ground…

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Q: 1 Find the length of the curve y (x2 + 2)3/2 from x = 0 to x =9. 3

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Q: Evaluate the triple iterated integral. xyz dx dy dz Jo

A: To evaluate the triple integral.

Q: | (2x - y) dx + (x + 3y) dy. Evaluate C: arc on y = x5/2 from (0, 0) to (4, 32)

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Q: Find the area of the part of the circle r = 8 sin 0 + cos 0 in the fourth quadrant . Answer :

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Q: Evaluate the triple iterated integral. r2 xyz dx dy dz

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Q: Find the point S so that ray (PQ) and ray (RS) are each of the same vector where P = (2, 5), Q = (1,…

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Q: A tank is being filled with a liquid. Z (1), given below, is the amount of liquid in liters in the…

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Q: Peaive marima and, minima, 4 any tar the funchno If there is not an answers write N/A Wde ms wefs as…

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Q: Evaluate the derivative of the function: x2 f(x) = ( x²+1 8x (æ²+1)° O 8a(a² –1) (2²+1) O 1 4x…

A: Use the chain rule for finding the derivative

Q: What is the equation of the tangent plane normal to x2 + y2 + z = 9 at the point (1, 2, 4)? O 2x -…

A: Given; f(x,y,z)=x^2+y^2+z-9  Point (1,2,4)

Q: Evaluate the line integral / (4x + 8y)d.x + (4x – 9y)dy along the curve C : x = 10 cos t, y = 20…

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Q: Evaluate F. dr. F(x, y) = 7xi + 8yj C: r(t) = ti + V4 - t²j, -2 sts 2

A: Use line integral concept

Q: 1) What are the equations (4 of them) that show the relationship between polar and rectangular…

A: We can solve as follows

Q: 2. The volume of the sun is 1.4 x 10 cubic kilometers and the volume of the earth is 1.1 x 102 cubic…

A: Earth mass

Q: complex form and COS U+ i sin o) be the polar form Idition and subtraction between two complex…

A: Topic:- complex number algebra

Q: 1+9n² 1. b) Determine whether the sequence a, =. converges or diverges. If it converges, 1+n² find…

A: 1/infinity=0

Q: Evaluate the following limit: x + 2 lim x→-3¯ x² -+ 2x – 3 O +∞ 10

A: The given limit,        limx→3-x+2x2+2x-3

Q: Sketch the region R and evaluate the iterated integral F(x, y) dA. (1 - 2x + 8y) dy dx 2.0- 2.0 1.5…

A: A detailed solution is given below

Q: 1. Suppose you are in charge of payouts for a competitive 10K race. You decide that the top 12…

A: (A) Solution:  In both options total amount is same i.e. $546,000 but option B situation will be…

Q: Find the arc length of the parametric curve. 4 cos(t), y = 4 sin(t), z = 3t; 0<t<T L=

A: Here we have to find the arc length of the parametric curve.

Q: Let i 1 and i and let w = ü x v. Answer the following: 5 Find w. Give your answer as a vector in the…

A: Givenu=0i+j+5kv=-2i+4j-5ka)Givenw=u×vw=ijk015-24-5w=i(-5-20)-j(0+10)+k(0+2)w=i(-25)-j(10)+2kw=-25i-1…

Q: Which among the choices is NOT true about the continuity of f(x)? if x 1 X, メ, 2 f(x) = (2 – x), O…

A: Solution

Q: Evaluate the integral (8x + 12y)dx + (9x – y)dy along the parabolic (8x +12y)dx + (9x – y)dy along…

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Q: Use substitution to find the Taylor series at x = 0 of the function In (1+3x*). What is the general…

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Q: Find the area of the region enclosed by the parabolas y=x and y=2x-x². Make a sketch and shade in…

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Q: Determine the value of the Wronskian W (y1, Y2) of y" – 2y +1 = e2 (x +1) if x=1.3 by using…

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Q: Determine whether each of the following functions is (a) continuous (b) differentiable 5. f(x) = 2x²…

A: Find your answer below

Q: Find y': y = /5+ 2x – x² - 1-x O y = V5+2x-a2 1 O y = 2/5+2x-a2 7-2x O y = 2/5+2x-a²2 O y = /2 – 2x

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Q: 6) y' = 2x-3y+4 x+y+2

A: Differential equation

Q: Given the function: x2-4 if x 2 f(x) = , 2-x if x = 2 What should be the value of k so that f is…

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Q: 2 4 Find an equation of the normal line to the curve 3x¯y' – x°cos(ny) + 4x + 2 = 0 at the point…

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Q: e. Suppose someone claims that C'(5000) = -0.1. What would the practical mean- ing of this…

A: We have to find the meaning of C'(2000).

Q: Exercise 7.2 1. Calculate the values for f (x) = 3x a) f(2) %3D b) f(-2) %3D is (1; 2; 3). 3. %3D of…

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Q: Find the volume of the solid that results when the region enclosed by the geviN curves. -2X ソニ e;…

A: The given curves are; y=e-2x, y=0, x=0 and x=1. So, the bounded region is as shown below. Now apply…

Q: Use the following information to answer the question below. lim f(x) = 3 lim f(x) = ∞ lim f(x) = -3…

A: Information of the function is given, we have to find the required values

Q: 3 da Evaluate a+2 A. 3 B. 2 С. 1 D. 0

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Q: Answer only option b.

A: Given, C is the consumption of fuel in litres per kilometer. s is the car's speed in kilometer per…

Q: dy Solve the differential equation = -3 cos x-4x if y(7)=0. dx

A: To solve the given differential equation.

Q: Let S1 be the hemisphere with Cartesian equation z = 6 – /36 – x² – y? and S2 be the upper nappe of…

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Q: What is the differential equation whose solution represents the family y = Ae3x + Be 3x+Ce4x? %3D O…

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Q: Let 7(t) = Find )dt (don't include the +C)

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Q: Find the area between the loops of the limacon r= 7(1+2 cos 0). Area =

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Q: Find the dimensions of the right circular cone of minimum volume V that can be circumscribed about a…

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y°x²j+2z²yk. %3D div F= curl F=

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Q: Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in North America…

A: Given problem:- Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in…

Q: | (2x - y) dx + (x + 7y) dy. Evaluate C: x-axis from (0, 0) to (0, -7) and (0, -7) to (4, -7)

A: x-axis from 0,0 to 0,-7 indicates that interval of y is from 0 to -7 y-axis from 0,-7 to 4,-7…