Perform the indicated integration using RATIONALIZING SUBSTITUTION 3 dy 4 + ³√y+1 1.f.

Q: if √x ≤ f(x) ≤ 4₁ x + 1 for all the positive x-values, then what is lim P(X) ?

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Q: Find a vector equation of a plane having x-intercept 4, y-intercept -1 and a z-intercept of 5.…

A: The x-intercept is 4 The y-intercept is (-1) The z-intercept is 5 So they can be written in ordered…

Q: Determine the derivative with respect to 'x' of: f(x) = Cos (sin x) - sin(cos.x)

A: We know that the derivative of sinx is cosx  And cosx is -sinx

Q: Given u = a. 27 + 47 b. u c. u x d. lul V V [-4,4, 4] and = - [-5,6, 2] find

A: Addition of two vector formula and product rules

Q: Calculate the linear combination. (Give an exact answer.) X = y = 6(4j+2k) - 4(2i + 7k) = (x, y, z)…

A: The vector is given by 64j+2k-42i+7k = x, y, z To determine: The values of x, y, and z.

Q: a) lim (-2x¹) = 8118 ) lim (-2x¹) = xx ) lim -√x = 118

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Q: Suppose the demand function for a product is given by the function: D(q) = -0.02q+98 Find the…

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Q: +(Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous equation.…

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Q: Find the plane determined by the intersecting lines. L1 x= -1+2t y=2+t z = 1 - 3t L2 x=1-4s y = 1+2s…

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Q: Each of the following problems addresses a course SLO for Math 21. Each individual student completes…

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Q: 2. Determine the cartesian equation for a line that passes through the point (4,-3) and is…

A: The line passes through the point 4,-3 and is perpendicular to the line r→=2,-3+t5,-7 Therefore, the…

Q: Find the maximum and minimum values of the function f(x, y) = xy subject to g(x, y) = x² + xy + y² =…

A: Objective function fx,y=xyConstraint function gx,y=x2+xy+y2-108

Q: Find the area between the curve y = y 2.0 1.5 1.0 0.5 1 square units y = 2 1 x5/4 1 X5/4 3 and the…

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Q: Consider the table below for lim (f (h)). Step 2 of 2: Find lim (f (h)). h-673" h 672.5 672.9 672.99…

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Q: If the velocity of a moving object is t 2 1² v (t) = 20 2 in meters per second, then what is its…

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Q: Use the table to the right to find the given derivative. d[ f(x) dx x+3 x=4 f(x) [X3] (Simplify your…

A: Given that ddxfxx+3x=4

Q: SO f'(2x) dx. +6 Lºx xf"(x) dx.

A: The given integral expression is:∫04 f'(2x) dx

Q: In this problem, y = c₂ cos(4x) + C₂ sin(4x) is a two-parameter family of solutions of the…

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

Q: I understand part A where g is not continuous, but I dont understand the differentiable part. Why is…

A: Given graph

Q: Problems In each of Problems 1 through 11: a. Seek power series solutions of the given differential…

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Q: Evaluate the definite integral. 7 7 4 X X-5 X X-5 dx = dx

A: To evaluate the following definite integral. ∫47xx-5 dx

Q: Find the arc length of y = (*2²)* + over [1,4]. 2(x+2)² (Use symbolic notation and fractions where…

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Q: Question 5 Which values fall within the range of this function? f(x) = -4x+3+2? Select all that…

A: To determine the value that falls within the range of  the following function. fx=-4x+3+2

Q: Find the distance from the point to the line. (-2,2,-4); x = 2+2t, y=3-t, z=-1-3t The distance is…

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Q: Use the Shell Method to compute the volume of the solids obtained by rotating the region enclosed by…

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Q: An general equation for the plane passing through the points (0, –1, 2), (−1, −5, 4), and (2, –4, 3)…

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Q: The total number of acres of genetically modified crops grown worldwide from 1997 to 2003 was…

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Q: Let a = (0, 1) and b = (4, -4). Show that there are scalars s and t so that sa + tb = (16, −17) You…

A: We have, a = ⟨ 0, 1 ⟩  b = ⟨ 4 , -4 ⟩ sa + tb =⟨ 16 , -17 ⟩

Q: Solve the given equation 3e*+2 = 75

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Q: √2 cos 0 + √2 sin 6, find the Cartesian equation of the tangent line v Given the polar curve r = to…

A: We need to find equation of tangent line.

Q: 1 (a - b) In (a − x) (b - x) X *)] = [K₂ t]

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Q: Sketch the graph of the following parametric equations. a. x = 4, y = sint b. x = e^t, y = e^2t, t ∈…

A: a) x=4 ,y=sint b) x=et,y=e2t ,t∈[0,∞) c)x=3sint,y=4cost ,t∈0,pi

Q: a. AOR: y = 0 b. AOR: x=0 c. AOR : x = 2

A: Since you posted multiple subparts, I need to solve only first three subparts.

Q: (a) Differentiate the following functions with respect to t: (i) (ii) y = 4t-t² t-1 y = esint 2+2.5…

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

Q: Given the function f(x) = -2x³ +96x + 1, determine the intervals where the function is increasing…

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Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: r=135 in h=168 in Rate of increase of radius=1.2 in/sec Rate of decrease of height=-2.8 in/sec

Q: If f is a differentiable function and f'(x) = x5-5x4+ 5x³+2, then fis concave up on

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Q: Is the line x = -8-6t, y = −8+9t, z = -9t parallel to the plane 3x+y-z=9? Give reasons for your…

A: To find the dot product of given line and find the line is parallel or not.

Q: Find all the first and second order partial derivatives of f(x, y) = 6 sin(2x + y) — 2 cos(x − y).…

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Q: Without using symmetry, determine a definite integral that represents the area of the region…

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Q: The power series representation of 1 3x + 2 is: f(x) =

A: we need to find the power series representation of the function f(x)=13x+2

Q: Find the vector parametrization r(t) of the line L that passes through the points (4, 1, 2) and (9,…

A: The line L passes through points 4,1,2 and 9,3,7

Q: A meteor follows a trajectory r(t) = (8,6,5) +t(7,6, -2) km with t in seconds, near the surface of…

A: A meteor follows a trajectory rt=8,6,5+t7,6,-2

Q: PRACTICE ANOTHER Solve the system of linear equations. (Enter your answers as a comma-separated…

A: x1-x2=0...............A 7x1-6x2=-1..........................B

Q: Solve the given differential equation by separation of variables. y In(x) dx = (y + ¹)² dy

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Q: J 3x ex dx

A: The given integral, ∫3xexdx. We have to solve this integral.

Q: 3. Use the Intermediate Value Theorem to show that there is some c in the interval (-1,0) at which…

A: f(-1) = (-1)³ - 3(-1) + 1 = -1 + 3 + 1 = 3.  f(0) = (0)³ - 3(0) + 1 = 0 + 0 + 1 = 1.

Q: Find two unit vectors that make an angle of 60° with  v = 3i + 4j.

A: We are required to find: Two unit vectors that make an angle of 60° with  v = 3i + 4j.

Q: Find equations of the normal and osculating planes of the curve of intersection of the parabolic…

A: The curve of intersection of the parabolic cylinders x = y2 and z = x2 at the point (1, 1, 1). Find…

Q: Suppose f(x) = 2 + 8x². Determine, in a simplified form, each of the following: (a) f(a) = (b)…

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