Evaluate

Q: Evaluate the following limits: z² + 4z – 12 z² – 2x 3. lim

A: 3) To evaluate the limit: limx→2x2+4x-12x2-2x

Q: Consider two vector equations ℓ1 : ⟨x, y, z⟩ = ⟨3, 7, 4⟩ + t⟨2, 3, 1⟩, for some parameter t, ℓ2 : ⟨x...

A: Check the Ratio of direction ratios of both the lines. 

Q: 25. - lim (tan x)*om

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Q: The general solution of 4lnxdx- xsec?ydy= A 21n2x – tany = C B 2ln?x+ tany = C (c) 4ln?x- sec?y = C ...

A: We have to solve the question  

Q: 3.2 2. 3t (t 8-4れt。75 ニ

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Q: Sx (x² – 2)14 dx

A: Use algebraic substitution to integrate then simplify. 

Q: A street light is mounted at the top of a 10 ft tall pole. A woman 6 ft tall walks away from the pol...

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Q: Perform the indicated operation and write the result in standard form. (3 – 5i) O-646. 4+ 958. 4i O ...

A: Simplification of

Q: Question 3 Use the method of Lagrange multipliers to find the minimum of f (x, y) = xy? subject to t...

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Q: Consider the graph of 7x2 4x + 4y? – 5y = 100. - - - 4x + 4y? – 5y If the graph of 7x? stretched hor...

A: Topic:- calculus

Q: f SinA Differential Equations 2. 10 A cos'x sin x dy + (y cos³x - 1) dx = 0

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Q: (a) f(x) =x² – 2r

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

Q: sin r lim ,3 81.

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Q: x-2| Find lim x2 x-2

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Q: Find the derivative of the function using the definition of derivative. State the domain of the func...

A: (a)        f(x)=x2-2x3f'x=limh→0f(x+h)-f(x)h=limh→0x+h2-2x+h3-x2+2x3h=limh→0h2+2xh-h3-6xh2-6x2hh    ...

Q: Find the relative minimum of this function f (x,y) = 13 – 6x + z? + 4y+ y? A. f has a relative minim...

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Q: For the following exercises, find the lengths of the functions of X over the given interval. If you ...

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Q: 00 T LO uonsan Find a formula in each part below for the number of zebra mussels in a bay as a funct...

A: topic - functions

Q: Write the vector (-5, -9) as a linear combination of the vectors (-2, 3) and (1

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Q: 1. If ü= (2,-3), v=(1, -5), and w=(6, 2), determine the following: a) |ü +v| b) 3 ỹ -ū +w

A: a) u→+v→=(2,-3)+(1,-5)=2+1,-3-5=3,-8=32+(-8)2=9+64=73|u→+v→|=73

Q: Find the product, if possible. 5 -3 0 5 2 1 4 6. Select the correct choice below and, if necessary, ...

A: The given product,     710-5465-321

Q: (xy2+y²) dx + sec2(1/y)dy=0 is alan A Exact DE B Homogeneous DE Variable Separable DE none of the gi...

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Q: Evaluate the position function r (t) if we have the velocity function and initial condi- tions. 1 6t...

A: Given

Q: Find the curvature κ of r(t) = at t = 0. Simplify your answer

A: use curvature formula for vector valued function.

Q: The graph of y =f (x) is given. Solve the inequality. f(x)<0

A: Given that: Graph of y=f(x)

Q: 2. Given f(x) = 3x – 2 and g(x) =+, find each of the following: (a) (f o g) (z) (b) (go f) (x)

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Q: -S; (4vw) dw

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Q: (x+1)dy = (2xe* - xy – 2y)dx

A: Solved below

Q: Find the general form of f if f'(x) = 5f(x).

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Q: 2. Find the polynomial f (x) of degree 4 whose graph is shown. Leave your answer in factored form. 1...

A: Since you have asked multiple questions in a single request we would be answering only the first que...

Q: 9- Use the triple integral to find the volume of the given solid (a) The tetrahedron enclosed by the...

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

Q: 29. x10; e0.01x 30. x² In x; In?x 31. 32. In x; In (In x) 33. 100%; х* 34. 35. x20, 1.00001* 36. x10...

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Q: Consider a function x-1 if x 1 (a) Find lim f (x) if it exists. If it doesn't exist, explain why. (...

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Q: v+1.57=3.13

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Q: a) Find the center-radius form of the equation of the circle with center (4, -2) and radius 7. b) Gr...

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Q: is dropped from a tower, 576 ft above the ground. The object's height above ground x seconds after t...

A: Topic:-  algebra   

Q: Find an equation for line that passes through point p(8,6) and perpendicular to v=2i+3j

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Q: 1. Solve the system by using A-1, the inverse of the coefficient matrix: x-3y+z =1 2х - у+ 2z %3D2 x...

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Q: Evaluate the limit 5(y? – 1) lim y→4 8y2(y – 1)°

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 2 cos(t) +...

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Q: Find the unit tangent vector T, and the unit normal vector N for r(t) = at t = 1. Simplify your ans...

A: We need to find the  unit tangent vector T, and the unit normal vector N for t=1.Below find the solu...

Q: The ratio of working-age population to the elderly in the United States (including projections after...

A: For the given function

Q: 41. Let f(x, y, z) =x?y+ y²z. Use the Chain Rule to calculate af/as and af/at (in terms of s and f),...

A: Since f is function of x, y and z.  For partial derivative f with respect to s and t we using chain ...

Q: The partial fraction decomposition of 4x 12 can be written in the form of 8x2 + 30x + 7 g(x) f(æ) + ...

A: We have to find the value of f(x) and g(x) 

Q: dg 5t – 7t2 | for g(t) = dt 2et

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Q: (I'o67 =7 %3D 2. of

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Q: Use the four-step process to find f'(x), and then find f'(1), f'(2), and f'(3). f(x) = 4 + 5-/x f'(x...

A: Given the query is to find the derivative of the expression using definition.

Q: A merchant can sell 60 items per day when he charges $1.60 for that item. He has observed that for e...

A: NOTE: Refresh your page if you can't see any equations. . A merchant can sell 60 items per day when ...

Q: 5. A ball is thrown vertically upward from the top of a 100 foot tower, with an initial velocity of ...

A: Given that position function is st=-16t2+10t+100 velocity =derivative of stvt=d stdt=d-16t2+10t+100 ...

Q: isometric version

A: