The angle between two vectors a = (1, 1, 2) and b = (-1, 2, k) is 60°. Find the value(s) of

Q: Find the generated volume f(x)=sin(x) and the lines x=0 and x=π and rotate about the x-axis V=π^2…

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

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Q: (1) Find the derivative of the function f(x) = 2x³ - 12x² +4 and use it to find the critical numbers…

A: Solution is given below:

Q: a. Find the linear approximating polynomial for the following function centered at the given point…

A: Given f(x)=1xa=1

Q: 14-Consider the Lie nard equation - (u-x²)x + x = 0. The Jacobian matrix for the linearized system…

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Q: Please correct me if i'm wrong. The points where f(x) appears to concave downward appears to be…

A: Given , the point where f(x) appears to be concave downward appears to be (-2 , 2.9 )

Q: a) 0 1:3 x dx -3√√9-x² V 2

A: The objective is to evaluate the integral.

Q: 4. Which of the following is f(x) = x² the parent function for? a) f(x) = x³ + 2x²-x+ 13. b)…

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Q: e) fx³ √2x² +1 dx wil(-) {. ub f CP

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Q: Find the sum by adding each term together. Use the summation capabilities of a graphing utility to…

A: We have to find the sum  ∑j=16 8j + 5.

Q: Evaluate both integrals of the Divergence Theorem for the following vector field and region. Check…

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Q: Part 1 A rectangular tank with a square bottom has base side lengths of 3 feet and a height of 10…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for you. If…

Q: sec¹ (3x) b) ›1$ 3 tan³ (3x) dx

A: I have stated the used formulas in the solution

Q: Solve the following system of equations using the Gauss elimination method 4x - 3y + 2z = -16 -3x -…

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Q: Use following se k Z K-I the integral test Series to decide converge

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Q: 9x²-4 :) Tax² ² (x² − 4)(x²+4) dx

A: Topic:- application of integration

Q: Consider the function f(x) = x² + 2x - 8 x - 3 a. Find the first derivative. f'(x) b. List any…

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Q: f(x) = -2x² + 7 7x 10 - if x ≤ −1 if x > -1

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Q: Find the the maclaurin following: four Series nonzero terms of the for each

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: JENCES AND SERIES: onvergent or divergent and, if convergen 23 an 20 ,n=1,2,3,...

A: The answer is given below:

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

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Q: 2.4 Write functions of the following graphs. 2.4.1 2.4.2 + -3 -2 -3 N 0 -1+ 34 2+ 0 - 2

A: Above question is solved

Q: 1 4. f₁² (1-x²) dx 5 2

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Q: er of cars produced when a dollars is spent on labor and y dollars is spent on capital invested by 1…

A: Topic:- application of derivatives

Q: 1. cos50 sin³0 de TL 2

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Q: 2. 3. (32²+7)dx=(2,₁¹²₁ )dy = 0 4) 1 xe²x dx + (5-1)dy = 0, y(0) = 0 1

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Q: Find the unit tangent vector T(t) for r(t) = 4ti + 7t²j + 3tk. T(t) =

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Q: f(x) = √x²-2 7+|x6| S if x < 2 if x ≥ 2

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Q: Find the shortest distance r1 between the two lines given by r₁ (t) = (3 + t, 3t, 5 – 4t) and r₂ (t)…

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Q: 1,-1, 3), 6 = 2-(0, 5, -2) Find 52 +22-46 C a Let a = O (5, 1, 1) *(5, 7, -1) O(18, 35, 12) O(-14,…

A: Topic:- application of algebra

Q: Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x² + y² = 4 and…

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Q: What is the general solution to the the differential equation3y "'-y'- 2y = 10e? A B v=C₂₁e (²/³) x…

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Q: 5₂00⁰ dx 2 3 1.

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Q: = 5, A2=3, A3=1 and A4=1

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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: Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 4x + 4 between x =…

A: Given function, y=4x+4 x=6, x=8 First we draw the diagram

Q: (3x²+2x-6)dx + e²ydy=0

A: Given Problem:- 3x2+2x-6dx+e2ydy=0

Q: Question 6 Determine the Fourier series for the function defined below: f(x) = 2x in the range x = 0…

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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: 4) Activity 5: Check for Understanding (10 mins) NOV ob For the equation of y²dy = x(xdy - ydx)e*/y.…

A: We can find the degree of the given function and differential equations.

Q: . Given TR = 45Q -0.5 Q², TC = Q³-8Q² + 57Q + 2, find out the level of : output at which firm…

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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: 4. y = x cos(In x) x²y" - xy + 2y = 0

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Q: A piece of cardboard measuring 13 inches by 12 inches is formed into an open-top box by cutting…

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Q: Find lim Ax-0 f(x+1 + Ax) = f(x) - Ax f(x) = 3x². - 9x Step 1 Find f(x + Ax) by substituting x + Ax…

A: Given  f(x) = 3x2 - 9x

Q: 1. Factor the following completely. a) 16x² - 100 b) 15x²-3x - 12

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Q: Imagine you want to enclose a field in the shape of a rectangle with a semicircle on one end. If you…

A: Imagine you want to enclose a field in the shape of a rectangle with a semicircle on one end. If you…

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: -) 1 = dx x (1-√x)²

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