Find the the macl following:

Q: Find the flux of F across S, [/F. Nds where N is the upward unit normal vector to S. F(x, y, z) =…

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Q: Find a vector with initial point (-4,-2, 1) and terminal point (-12, 5, -8). Then find a unit vector…

A: Given problem:- Find a vector v→with initial point -4,-2,1 and terminal point -12,5,-8.Then find a…

Q: Find the cross product u x 7 where u = 51 -3j+k and = (-1, -3,2). uxv=

A: To find the cross product u→×v→ where u→=5i-3j+k and v→=-1, -3, 2.

Q: Let à = (-2, 2, 3) and 6 = (4, - 1,5). Find the projection of b onto a. proj, b =< Check Answer

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Q: The area of a square is increasing at a rate of 56 centimeters squared per second. Find the rate of…

A: Given data÷ Rate of change of area  =dAdt=56cm2/s Side of square =a=4cm We need to find dadt=?

Q: 3. Find the vertex, focus, and equation of the directrix for the conic given by (x + 1)² = -20(y -…

A: We have to find focus, vertex and equation of directrix.

Q: Find the Taylor series generated by f(x) = 6 sin 5 at x = 0.

A: Answer is in next step.

Q: Let 7 (t) = Find 7' (t) 7' (t) = Check Answer >

A: Solution ) r(t) = &lt; -3t5 + 5 , 4e-4t , 3sin ( -3t ) &gt;  r'(t) = &lt; d/dt (-3t5 + 5) ,…

Q: Which of the following IS NOT parallel to HA A B H F E C D

A: Given figure:-

Q: 1 6. √₁² √ 1 - √u du

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Q: (a) Find an affine change of coordinates that takes the unit square with vertices in the uv-plane to…

A: (a) The vertices of uv-plane is given as , P*=0,0 , Q*=1,0 , R*=0,1 , S*=1,1 and the vertices of…

Q: Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for…

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Q: Evaluate the integral. 7 7 √49-x² ILL 1 /49-x² (x² + y²)1/2 dy dx dz =

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Q: Find the differential dy of the given function. (Use "dx" for dx.) x + 7/7/7/72 dy= (3x72xx)dx y =…

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Q: 4. Which of the following functions grows at the same rate as 3^ as x g O 2x O√√3x +4 3* O √6x 0x +…

A: To compare the rate of growth between the given functions lets draw their graphs. Given function 3x,…

Q: Problem 1. You are fencing in an area next to your house so your cats can lounge outside. The cat…

A: We have given the length of material that is avialble for fencing is 27 feet.

Q: Use any method to find the volume, V, of the solid obtained by rotating the region enclosed by the…

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Q: Find a vector with initial point (4, -4,0) and terminal point (7, -14, - 10). Then find a unit…

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

Q: 1261 (2x+1 dz 4-3x -x² 1 (((x+) dx (3) 28 (2x-3 dx √(x²-1) (2x+3) 31 32 33 dx √(x²+1) (2x+1) alx…

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Q: = Approximate the area under the curve y with 4 subdivisions. x³ from x = 2 to 4 using a Right…

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Q: The function f is shown below. What is the value of nswer in simplest form. -8 -3 N 3 H N W 4 in -5…

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Q: Evaluate the limit of the given functions. 3x² - 17x+ 20 25x + 36 1. 2. lim x+44x² t³-1 1 lim t-1…

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Q: A tank half-filled with water is in the form of a rectangular parallelepiped 5 ft deep, 15 ft wide,…

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Q: Problem Set question: The position function for a falling objects is given by s (t) = -16t² + vot +…

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Q: TU 2. fz sin² x cos4 x dx J

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Q: 2022" + n 2022 (d) lim sin 2022! + n!

A: Apply the limits to solve

Q: MATH401 Question 3|- functions and numbers A. Prove that cos-¹(-x) = π cos-¹(x) for any real number…

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Q: Let a = (-5, 1, 2) and 6 = (2, - 1,3). Find the angle between the vector (in radians) Check Answer

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Q: Solve the differential equation (1 + y² + xy²) dx + (x²y + y + 2xy) dy = 0

A: Solve the exact differential equation  1+y2+xy2dx+x2y+y+2xydy=0

Q: Question 1 Find lim f(x) given the graph of f(x) shown below. x-5 +++ -10-9-8-7- Y 3 4 5 6 7 9 10 x

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Q: Evaluate the triple integral -3pi D x dV where E is the solid bounded by the paraboloid x = 6y² +…

A: Solution is given below:

Q: 12. What transformations are applied to the parent function f(x) = x² to obtain the graph of the…

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Q: Find the Indefinite Integral and check your result by differentiation. (Use C for the constant of…

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Q: d) Hence form a conjecture for the derivative of functions in the form y = (ax + b)². e) Prove your…

A: As you have mentioned I am answering Question (d) and Question (e)

Q: Question 2 Compute the following limit. Give your answer as a simplified radical, if necessary. lim…

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Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an…

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Q: 5. Find using first principles the slope of the tangent to f(x) = x² + 6x + 9 at x = -3.

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Q: Find the second derivative of the vector-valued function r(t) = (4t+ 6 sin(t))i + (6t+ 3 cos (t))}…

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Q: Find the arc length (s) of the curve r(t) = (3t, 2 sin(2t), 2 cos (2t)) for -4 < t 5 S = Check…

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Q: The Ratio Test can be used to determine whether O True O False converges.

A: Given ∑1n3

Q: 3. Evaluate f(x) = 15 – ½ (x) for f (4). a) 16 b) 14 c) 13 d) none of the above

A: 3.  This is a problem of polynomial.  Here given a polynomial f(x) and find f(4).

Q: Use calculus to find the open intervals on which the function f (x) = x +4√1 − x is increasing or…

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Q: Let P be the set of positive real numbers. One can show that the set P³ = {(x, y, z)|x, y, z € P}…

A: The objective of the question is determine the vector .

Q: The graph of f(x) is shown (see figure). 2X f(x) = (a) Find the following limits. L = lim f(x) = V…

A: According to guidelines, we must answer only three of the multiple subparts given. So, I answered…

Q: Which of the following functions will have a dashed line for the graph? y ≤ 4x^2 + 1 y = 4x^2 + 1…

A: Question : Which of the following functions will have a dashed line for the graph? 1. y ≤ 4x^2 + 1…

Q: Consider the following function. f(x) = (x-8)e* (a) Find the critical numbers of f. (Enter your…

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Q: Evaluate the integral by making the given substitution. [sec (3x)tan (3x)da, u = 3x +C

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Q: ∞ e4y dy

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Q: Let a = -17 +83 +9k and b = -87-23 + 3k. Find a b Check Answer

A: Given vectors are a = -1i+8j+9k and b= -8i-2j+3k Find:- a.b

Q: d) f(a) = (2a-1)² 2a + 5a

A: Solution ) f (a) = ( 2a - 1 )2/2a  + 5a  We know that  ( a - b )2 = a2 - 2ab + b2 f(a) = (4a2 - 4a +…