Show that the three functions: f₁(x) = ex-8f₂(x) = exf3(x) = 4(2x-2) are linearly dependent.

Q: As you are walking in the forest you look up just as a boulder becomes dislodged from the side of a…

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Q: Let P be the point with Cartesian coordinates (6, 9), and C be the plane curve with parametric…

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Q: Using trigonometric substitution to solve x-2√4 – x²dx = f f (0)d0. What is (a − b + ²)? A B U D I…

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Q: I the slope of the tangent line to the parametric curve X = 3 cos (t) y = 2 sin(t) ㅠ R 4 at the…

A: Given query is to find the slope of the tangent.

Q: Let C be a curve with the parametric equations à = − ln(t + 1); y = sint, t = [0, 1]. a. Set-up the…

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Q: a continuity of the function esinx (x,y) # (₂) X (X,Y)= (0,0) Discussion Sexiy) at the Point (0,0),…

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Q: Find the volume generated by revolving about the y-axis the area bounded by y2= x-2, y=x-4 Use shell…

A: Here we have to find the volume by using shell method.

Q: Solve f(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

A: Solved below.

Q: Find the moment of inertia: x = y +1; y = 1; y = 2; x = 0 about x-axis.

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Q: (b) The function y(x) satisfies the inhomogeneous second order linear differential equation d²y dy +…

A: We have to find the general solution of the given differential equation using variation of…

Q: Find a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² -z = 0…

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Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: This question can be solved using the concepts of application of derivatives.

Q: 2r find the moment with respect to the wavic of the area hounded by the parabola v - Av-172 and v

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Q: A product can be produced at a total cost of C(x) = 500 + 100x² + x³ dollars, where x is the number…

A: Solved below.

Q: Determine if the function f (x, y) = if (x, y) = (0,0) is continuous at (x, y) = (0,0). If not,…

A: Use limit to find wheather function is continuous or discontinuous.

Q: Starts the domain, vertical asymptote, and end behavior of the function.  g(x) = ln(3x +21) + 1.5…

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Q: = Find the area bounded by the curves -x + y² = 8, x = -2y and y

A: Follow the procedure given below.

Q: Let f(t) = (0 if 0 ≤t<3 (t-1 if 3 ≤t By using the definition of the Laplace transform we find that…

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Q: Let The coefficient of x' in the Maclaurin series for f(z) is: Answer: . You may explain your answer…

A: Note that, the power series of ex is: ex=1+x+x22!+x33!+...

Q: 9 Determine the area to the right of g (y) = y² +4y-5 and to the left of the y-axis.

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Q: Find f. f(t) = 5e¹ - 6 sin(t) — 5 f"(t) = 5et + 6 sin t, f(0) = 0, f(π) = X 0

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Q: II. Consider the circle C1 : r = 1 and the roses C2 : r = cos 2θ and C3 : r = 2 cos 2θ, each of…

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Q: Find the Area of the Surface obtained by rotating the curve about the x - axis y = cosh x, 0≤x≤1

A: Area  of surface is obtained.

Q: Area of the Region and Volume of the Solid of Revolution Given: The region is bounded by the curves…

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Q: Find the area bounded by the parabolas (x - 2)² - 9py = 0 and y² = 9p(x-2).

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Q: f(x)=8x¹-7x³+2 on [−2,1]

A: To compute the average value of the given function f(x)=8x4-7x3+2 on [-2, 1]

Q: -x+1 3+z Given the points R (1, -1, -3), the vector v = and the line d: = 1 + y = 3 2 1. Determine…

A: Both questions are solved.

Q: 3. Let 7 and w be vectors such that v=(2, 2, -1), |||| = √2, vw=-3, and × = (2,-1, 2). a. If u =…

A: Key points: We say that 2 vectors are orthogonal if they are perpendicular to each other. If two…

Q: d The series is divergent. . Ignore "Give your reasons" below. There is no need to give reason.…

A: False , we this sum is convergent

Q: 3x + 2y = 6; x = 0; y = 0; axis OY. Find the moment of inertia.

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Q: example of properties of definite integral

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Q: Find the volume of the largest right circular cone that can be incribed in a sphere of radius 3. 3 y…

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Q: f(x)-f(a) a. Use the definition mtan = lim x-a x-a b. Determine an equation of the tangent line at…

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Q: (-1)k 9. Does the series Ex=1 +7 converge absolutely, converge conditionally or diverge? A.…

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Q: 3 [(V) dt -

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Q: Given x - ³²+2y — In(y + 1), find the arc length for 0 ≤ y ≤4 8

A: The arc length of the curve x=f(y) for a≤y≤b is given by ∫ab1+dxdy2 dy

Q: Find the volume of the solid generated by the region bounded by y - x² = -3, x+y = 3 about y = -5.

A: The equation of the curves are given by C1: y-x2=-3 ⇒y = x2-3 C2: x+y=3 ⇒y=3-x To evaluate: The…

Q: S N

A: Use ratio test for checking the radius of convergence

Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

A: topic - application of derivatives

Q: [xv x√2x + 1 dx

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Q: Find the area of the region bounded by y=x²-1, x=2 and y=0. Use horizontal element and express area…

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Q: 3. z = x+y x-y

A: Given:        z=x+yx-y Partial derivative with respect to x:      ∂z∂x=∂∂xx+yx-y      Treat y as…

Q: The population of a town is decreasing at a rate proportional to its size. In 1980, the population…

A: The population of a town is decreasing at a rate proportional to its size.In 1980, the population…

Q: Given x = y³+2y — In(y + 1), find the arc length for 0 ≤ y ≤ 3 B

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Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. 1 S₁° 19 dx…

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Q: 26. What is the value of lim A. - 2 B. - 1 1-cost t→0 t C.0 D. 1 - ?

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Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim x x→0+

A: We have to determine limit by useing l hospital rule

Q: _ ²+2y — In(y + 1), find the arc length for 0 ≤ y ≤ 3 8 Given x =

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Q: Solve ²₂(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

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Q: Consider the function. x³ + 12 f(x) = X Determine the intervals on which f is increasing,…

A: A function f (x) is increasing on the interval I if f'(x) &gt;0 for x in I. A function f (x) is…