Find the value of f(-1) when ƒ"(t) = 6(2t − 1) and ƒ'(1) = 6, ƒ(1) = 1.

Q: The distance an object falls (when released from rest, under the influence of Earth's gravity, and…

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Q: Question 2 Find y' given 2 + x¹y² = y sin¯¹ y²

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Q: Evaluate the limit assuming that limx→4 g(x) (Use symbolic notation and fractions where needed.)…

A: given limx→4g(x)=-5

Q: Find f(x) if f(0) = 1 and the tangent line at (x, f(x)) has slope 3x

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Q: Use scratch paper to complete the table below, and guess the value of the limx→12²-144 f(x) x f(x) X…

A: Here  f(x)=x3-1728x2-144 To determine  limx→12f(x)=limx→12x3-1728x2-144

Q: The First Gate Having crossed the room, you find yourself at another gate with a required passcode.…

A: The function is fx=6x2-24x+2 on the interval -4,4.

Q: Evaluate the limit assuming that limx→-3 f(x) = 5 and limx→-3 g(x) = 1. (Use symbolic notation and…

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Q: Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west…

A: Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west…

Q: Use Theorem 2.1.2 to find the slope of the tangent line of f-1 at x = -1. Given f(x) = -2 + 4x/x + 3…

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Q: Find the тся value of the function f (x₁y) = x+2y subject to the constraint x² + y² = 3 using…

A: We want to maximize the function f(x,y) = x+2y subject to the constraint x² + y² = 3. Using Lagrange…

Q: The graph below is the function f(x) -5 -4 -3 2 24 1 +2- -3 -4 -5 Find f(-1) Find lim f(x) I-→-1 1 2…

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Q: Evaluate the limit numerically or state that the limit does not exist. (Give your answers as a whole…

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Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. (a) 27 (b) 90…

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Q: Let T: U →U. A vector u is a fixed point of T if T(u) - u. Prove that if T is linear, the set of…

A: Let  t:U→U. A vector u is a fixed point of T if T(u)=u. Prove that if T is linear, the set of fixed…

Q: 69. 1 S² 0 xe-x/2 dx

A: The given integral is xe-x^2/2 limit from 0 to 1.

Q: x²-4 lím x→∞0 x²-x-2

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Q: e linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

A: Thickness of paint = 0.01cm Diameter of hemispherical dome is 60 meter

Q: (Use symbolic notation and fractions where needed.) lim (3x³ + 7x²): = x→

A: we will find the required.

Q: a = ci + j and b = 16i + 12j. Find c so that the angle between a and bis- und your answers to four…

A: a=ci+j b=16i+12j.

Q: Find the domain of the function f(x)= {xlx>3} 7/3

A: given function is :-f(x) = x23then we have to find its domain

Q: n=1 n! (x - 10)³n gn

A: series

Q: Question #3 - What is the derivative for the function f(x) = ln (x²)? d) f'(x) = ² X a) f'(x)=- 1 a)…

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Q: Find the general solution of x2y" - xy' + y = x ln (x)

A: The given differential equation is:x2y''-xy'+y=x ln(x)

Q: Estimate the slope of the tangent line at the point x = 8, for f(x) = ln(x). (Use decimal notation.…

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Q: Find the average value of g(t)=12+6t over the interval [0,3]. Round your answer to the nearest…

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Q: Consider the function fand its derivative below: f(x) = 2√x-5-(x²-10x + 5) and f'(x) = 5(x-7)(x-3)…

A: The critical point is the point where the derivative is zero or undefined and the function is…

Q: The greatest integer function is defined by [x] = n, where n is the unique integer such that n ≤ x <…

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Q: Determine a vector equation for each line. a) perpendicular to line 4x - 3y = 17 and through point…

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Q: Determine the interval on which the function in the graph below is decreasi -12 -10 -8 O a. [6, 10]…

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Q: The graph of f is shown below. Evaluate each integral by interpreting it in terms of areas. 3 2 1.…

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Q: You are standing above the point (2,5) on the surface z = 30 - (2x² + 2y²). (a) In which direction…

A: z = = 30 — (2x² + 2y²).

Q: Find the absolute maximum and absolute minimum of the function f(x) = 5x² – 30x + 1 on the interval…

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Q: 7. y = ex + 2, - хо =-1

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Q: 2x+y 5x+6y Find [/02/53 -dA, where R is the parallelogram enclosed by the lines R 2x+y=0, 2x+y=9,…

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Q: The percent P of defective parts produced by a new employee t days after the employee starts work…

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Q: 2 5 If the directional derivative value (Duf) of the function f(x,y) = x²-3x4 + 4y at Point (-2,0)…

A: Let (u) = Ai + Bj be the unit vector in the direction of the directional derivative at the point…

Q: Evaluate sec(). Give your answer in exact form (no decimal equivalents).

A: According to bartleby guidelines we supposed to do the first one of multiple questions  kindly…

Q: A man is walking away from a light source located 20 feet from the ground at a rate of 2 feet per…

A: We need to find rate of shadow moving.

Q: Use linear approximation, i.e. the tangent line, to approximate 1/0.202 as follows: Let f(x)=1/x and…

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Q: 14 Approximate (x²-3) dx using 4 rectangles. 2 It is approximatley (If necessary, round to two…

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Q: 4. Given that g'(x) = sinx(1 - 2cosx) determine the intervals over which g(x) is increasing and over…

A: We have to find the intervals over which g(x) is increasing and decreasing.

Q: As machines get older, the cost of maintaining them tends to increase. Suppose for a particular…

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Q: Evaluate each of the following limits: (a) lim (2+³) (b) lim (2t-³) t→∞ ∞047 (c) lim (2+³) t→0+

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Q: Solve the differential equation using laplace transform: y" +4y=F(t) where: F(t)=1, 0<t<1 = 0, t≥1…

A: The given differential equation is:y''+4y=F(t)where:F(t)=1       0&lt;t&lt;10t≥1y(0)=0,     y'(0)=-1

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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Q: Use the remainder theorem and synthetic division to find the value of f(x) where x is -3. f(x) =…

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Q: Find f, and f, for each of the following 12) f(x, y)=3x²y³ +2x−3y²

A: fx,y=3x2y3+2x-3y2

Q: 4. A rectangular pen is to be built with 1200 m of fencing. The pen is to be divided into thre parts…

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Q: What is the largest interval containing zero on which f(x) = sin x is one-

A: A function f: X -&gt; Y is said to be one-to-one, if the images of distinct elements of X under f…

Q: Show that the bound in Ore's theorem is sharp in the sense that for infinitely many integers n,…

A: step:1 Ore's theorem states that if G   is a simple graph of order n (n ≥ 3)   and for every pair of…