Divide using long division. State the quotient, q(x), and the remainder, r(x). (4x³+4x²-29x-15) + (2x - 5) ... + possible (4x³+4x²-29x-15) + (2x-5)= 2x-5 (Simplify your answers. Do not factor. Use integers or fractions for any numbers in the expression

Q: Use implicit differention to find an equation of the tangent line to the curve at the given point…

A: Derivative is the key for such problems

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A: Volume of the solid generated by a region R bounded above by y(x)=f(x)  and bounded below by y=g(x)…

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A: Given

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Q: Find all solutions of the equation 25 = -4i√//2. Give the modulus (which should be the same for all…

A: The objective is to solve the above question.

Q: Find the domain, range and graph it. f(x, y) = log(x²-3(y+2)) x+y-1

A: Domain: Domain is the set of all inputs to a function. Range: Range is the difference between the…

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Q: 2. Let f(x, y) = Give the exact value of the following and simplify to lowest terms. a) f (1,2) b)…

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Q: Find the vector component of v = (4, -1, 7) along b = (2, 4, -4) and the vector component of v…

A: Given; v=<4,-1,7> and b=<2,4,-4>.

Q: f'(2). f(x) = f* (2t - 3) dt

A: Topic:- application of derivatives and integration

Q: Use implicit differention to find an equation of the tangent line to the curve at the given point:…

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Q: Please see attached and : Find the domain and range of g. (Enter your answers using interval…

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A: Please refer to the image below

Q: Consider the parallelepiped with adjacent edges Find the volume. V = i u = 7i+ 5j + k v = i + j + 6k…

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Q: Suppose - 3x² +24x-53 ≤ f(x) ≤ 3x²-24x +43 for all x values near 4, except possibly at 4. Evaluate…

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Q: Find the point at which the line r(t) = (6, − 8, 1) + t(4, 7, − 2) intersects the yz plane. -

A: Here we have to find the point of intersection

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Q: Select the correct graph of the derivative of the function f(x) given below. -4 -2 -2 -4 12 4 X

A: Solution: Given figure is

Q: Identify the equation as a homogeneous or exact equation differential equation. then solve the…

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Q: A table of values for a one-to-one function is given. Find the indicated value. f-1(f-1(1)) = X f(x)…

A: find f-1(f-1(1))

Q: Consider the following. y = 12,7] (a) Sketch the graph of the function, highlighting the part…

A: Given that       y = 1/x , [2,7]

Q: 3. Let r : R → R² with r(t) = x(t)i + y(t)j where x(t) and y(t) are both twice differentiable. (a)…

A: We are given function r : R ->R2 with  r(t) =x(t)i + y(t) j Where x(t) and y(t) are twice…

Q: 7) In recent years, many states have passed laws against smoking in public buildings. The total…

A: Solution: We have, N(t) =501+19e-0.4t

Q: Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify…

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Q: For y = 1/x^2 , use differentials to approximate the change in y when x changes from 4 to 4.125.…

A: Topic- differentials WE are given y=1x2and x changes from 4 to 4.125and we know thatddxxn=nxn-1

Q: Suppose that the distance an aircraft travels along a runway before takeoff is given by D=(5/2)t²,…

A: Derivate D to find the speed and then equate that with the given speed to find the time.

Q: Locate the absolute extrema of the function 2x+4 g(x)= on the closed interval [0, 4]. 3 Select one:…

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Q: 3. Find the general solution to the DE (x+m) dy =(nx - py) dx where m, n, and p are constants.…

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Q: S² Sxx-6-dx 2 (x²+2 + = ²3 ) dx X-3 Sx x²-x-6 Sx (x+2)(x-3) A X=-2 = [2ln lx+21+31n/x-31] 21n/2+21+…

A: Topic:- algebra

Q: a. Calculate the first 5 terms of the sequence an = (1+1)", expressing your answers as fractions and…

A: Given sequence : an=1+1nn

Q: Suppose that the height of a particle is given by s(t) seconds and the height is measured in meters.…

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Q: Find the derivative dy/dx by implicit differentiation √x + y = 1 + x2y2                     (the…

A: Point to remember:- y is a function of x

Q: Determine the local maximum and minimum values of f(x)=2x³+3x²-12x+4 using the second derivative…

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Q: Find the four second partial derivatives of the following function. 5 6 h(x,y)=x² + xy +9 2h ax² 2h…

A: As we know that; The Sum/difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 And c·f'=c·f', where…

Q: Using the squeeze theorem, evaluate: lim h2 + cos(h) h--> -∞ 5 + h - 2h2

A: Solution

Q: Use the Chain Rule to calculate the partial derivatives g(x, y) = sin(x² + y²), x=3v- 3u, y = 4u +…

A: By using chain rule to calculate the partial derivatives ∂g∂u, and ∂g∂v.gx, y=sinx2+y2, x=3v-3u,…

Q: Find the derivative of y = 5x²sec 1(2x-3). O y'= 10x sec-¹(2x-3) + O y'= 10x sec-¹(2x-3) + O y'=…

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the…

A: Solution

Q: A particle moves along the x-axis so that at any time t≥ 0 its position is given by x (t) = (at)²,…

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Q: Section 4.1 Problems In Problems 1-8, find the derivative at the indicated point from the graph of y…

A: To find derivative of the given function.

Q: Compute the divergence and the curl of the following vector field. V = x sin y î+ cos y ĵ + xyk

A: given vector field=xsiny, cosy, xy

Q: C Find the domain range x and y intercepts, vertical and horizontal asymptotes, and zeroes of the…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges giver 1 by the vectors u, v and w…

A: Volume of tetrahedron =16u.v×w Given vertices P-5,6,0,Q2,1,-3,R1,01,S3,-2,3

Q: Find the unit vector u in the direction of (2, - 2) Give EXACT answer. You do NOT have to simplify…

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Q: f(t) = { t + 1/₁ 0 <t <2 2 ≤ t ≤ 10

A: