Given the vectors v=3i - 2j+5k and w=-i +4j+2k, find the following: a) 2v-w= b) V•W= ||w|| = c) 12 = d)

Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) The line…

A: Given problem:- Find a vector equation and parametric equations for the line. (Use the parameter t.)…

Q: 8.A kite at an altitude of 200 ft. moves horizontally at the rate of 20 ft/sec. At what rate is the…

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Q: The sum of two positive numbers is 20. Find the numbers if the product of the square of one and the…

A: We have to solve above question and the find the two number

Q: a²z 7.Find of z = 2x³-5xy² xy

A: Given double differentiation. First we find the partial derivative of z w.r.t y. Then we find the…

Q: find the equation of the tangent line to the graph of f(x)=x^2(x^1/2 +1) at x=4

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Q: The area of a square with side s is A(s) s². What is the = rate of change of the area of a square…

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Q: 3. Let u = f(x, y), x = r cos 0 and y = r sin 0. Show that: 1 1 Urr + −Ur + - U00 = Uxx + Uyy. p2 r

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Q: Suppose that R is the finite region bounded by f(x) = 2√x and g(x) = x. Find the exact value of the…

A: The given curves are: fx=2x and gx=x (a). So, the bounded region is as shown below;   Apply the…

Q: Evaluate the integral. (Use C for the constant of integration.) +² | dx 81-x²

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Q: Find by implicit differentiation, given that x²y - 2y4 = -4. Your answer could involve both x and y.…

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Q: Evaluate x + 2 S -dx using rationalizing substitution. Which of the following statements is correct?…

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Q: Evaluate the double integral over the given region R. xy² dA 2 X + 1 R xy² SS. dA= +1 R (Type an…

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Q: Q6: Find the Fourier coefficients and Fourier series of the function f(x) defined by -HAXNO f(x) = 0…

A: Here, the given piecewise function is: f(x)=0; -π<x<0x; 0<x<π and the period L=2π

Q: Using a particular trigonometric substitution 2 1 + x dx √3 +1-V 4 26 π - the above 1+ 13₁ 2 √1-x²…

A: To solve the given integral.

Q: Set up the integral, given area enclosed bewteen curves y= x^3 + 2x^2-8x and y = -x^2 + 2x

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Q: f cot rda Hint: 1. Final answer should be in terms of cosecant. 2. Any constants that arises due to…

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Q: cscxdx 5+ cos²x sin²x

A: solution:-∫csc25+cos2xsin2xdx,    {…

Q: Determine the volume of the solid generated bounded by x²= 2y and x= revolved about x=4. 2 Use ring…

A: Given problem:- Determine the volume of the solid generated bounded by x2 = 2y and x = y/2 revolved…

Q: Q3. Determine whether the function is continuous at x=1 or not (x² - 1 x = 1 f(x)=x-1 2, x = 1

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Q: Write TRUE or FALSE before each statement. Solve y dependent variable. differential equation.…

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Q: Consider this function: f(x) = 2x³ +5x² - 4x - 3 This problem has four parts. Be sure to answer all…

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Q: Find the area of the parallelogram with vertices A(-3, 0), B(-1, 3), C(5, 2), and D(3,-1).

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Q: Consider the function 2x+6 f(x)= x²+6 Find the critical point(s) off. (Give yourans wer in the form…

A: f(x) =(2x+6)/(x2+6)  Find:- Critical points  Local maximum and minimum at x= Interval function…

Q: dw For the given functions, (a) express as a function of t, both by using the chain rule and by…

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Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

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Q: Differentiate the function and express the final answer in factored form.  f(x) = (2x^3 +…

A: f(x) = (2x3 + 7)100 (3x2 - 8)50 f'(x) = 100*6x2(2x3 + 7)99(3x2 - 8)50 + 50*6x(3x2 - 8)49(2x3 + 7)100…

Q: Calculate M6 for f(x) = √7x on [0,2]

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Q: Solve the following problems. Enclose final answer. 4 4. Given z = x-y, Find az/ax x+y

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Q: Using the definition of the derivative, find f'(x). Then find f'(1), f'(2), and f'(3) when the…

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Q: dy 9 Find the general solution of the differential equation: - dt t Use lower case c for constant in…

A: Here we have to find the general solution of the given differential equation,  dydt-9t·y=t5 Compare…

Q: Using polar coordinates, evaluate the integral sin(x² + y²)dA where R is the region 1 ≤ x² + y² ≤…

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Q: 5. Let f(x)=log, (x+1). a. Complete the table of values for the function f(x)=log, (x+1) (without a…

A: We are given f(x) = log3(x+1)  We have to find  Values of f(x) for following values of x without…

Q: 7- Find fx³√3 - 2x² dx

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Q: 2. Find the limit and confirm your answer using the sandwich theorem 1 - cos x lim 818 1. 2. 3. 4.…

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Q: 5. Lim xsinx x+0+

A: Consider F=limx->0+xsin x Taking logarithm on both sides

Q: Find the parallel projection of the vector v = onto the vector w=.

A: Given problem:- Find the parallel projection of the vector v=<4, -5, 7> onto the vector…

Q: Find the derivative of g(t) = 4t2 + 8t at t = 3 algebraically. g'(3) =

A: Topic:- derivatives

Q: In your own language, describe the pattern of the following sequences (The sequences are given as a…

A: We draw required connection between the pattern and formulas as below.

Q: Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form…

A: Substitute f(x) in the limit formula

Q: y = f(x) denote the function defined as x²+x-2, if x < 1; f(x) = 1 X, if 1 ≤ x < 2; √x – 1, if x ≥…

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Q: Find f'(-2) if f(x) = 3 -7x. f'(-2)= (Simplify your answer. Type an integer or a fraction.)

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Q: 11. In each part state the x-coordinates of the inflection points of f. Give reasons for your…

A: We want to find inflection points.

Q: In problems 5 and 6 find the particular solutions of the given differential equations. d²y dy +9y =…

A: To find the solution of the given differential equation.

Q: 1. f(x) = cos (-:-)

A: From graph, it is clearlimx→∞cos1x =limx→-∞cos1x = 1

Q: √√√x ²-1 d For the integral What is the re-write of this integral? Ⓒ / - A z² dz 2(z² + 1) B…

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Q: 5- prove that - for sin Ꮎ dᎾ cose Ꮎ dᎾ

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Q: 7) y = — - cos (40-32) 2 D

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: S dx . Consider ½/₂ Using rationalizing substitution, what will be z and its corresponding integral?…

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Q: A street light is at the top of a 13 ft tall pole. A woman 6 ft tall walks away from the pole with a…

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Q: Numerical Integration: 2 1 Jo √x 1. =dx

A: We can find the answer as below