Find the components of the vectors. (a) (1,5) (4,1)

Q: f(n)(x) = = (−1)n+13n (n − 1)! (3x + 5)

A: Consider a statement P(n), where n is a natural number. To validity of P(n) for every n, use the…

Q: EC2: Verify that y₁ = 2³ and y., = |aare linearly independent solutions of the differential equation…

A: Two solution are said to be linearly independent if neither function can be put as a constant…

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i - 4j as…

A:

Q: A tank contains 100 gal of fresh water. A solution containing 5 lb/gal of soluble lawn fertilizer…

A:

Q: Simplify tanh(ln(6x))

A:

Q: Evaluate sinh -1(4/3)

A: Given: sinh-1(4/3)

Q: 5. Set up the integrals for the volumes of solids of revolution by revolving the triangu templates…

A:

Q: A solid is formed by rotating the region in the first quadrant of the xy-plane y = e2 + 1 and x =…

A: We need to find out the volume of revolution.

Q: calculate the derivative.

A:

Q: A trough 5 feet long and 1 foot high is filled with water. The vertical cross-sections of the trough…

A:

Q: If ƒ(x) = 5 + 4x − 5x², find ƒ'(0).

A:

Q: 3. Find the intersection of ₁ and ₂: ₁2+ 4y-32= -9 ₂: 4r +9y+2z=-1

A: Given planes equations:- π1: x+4y-3z=-9π2: 4x+9y+2z=-1

Q: Find the equation of the tangent line to the function y = − x² + 7 at the point (-1,6). No decimal…

A:

Q: Find the differential of the function. y = √5-t8

A:

Q: Graph the set of points whose polar coordinates satisfy the equation = 8 5x Choose the graph that…

A:

Q: Make a table of values that shows the function values of f(x)=x²-1 together with those of g(x)=3*…

A: f(x)=x2-1g(x)=3x

Q: A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the…

A: Given, A norman window has the shape of a semicircle atop a rectangle so that the diameter of the…

Q: Let f be a function defined as f(x) = {₁/2²) Note that e≈ 2.72. The value of f'(4) is approximately:…

A: Given:  fx=xex2+8 if x<24x2x+32 if x≥2 To Find:  To evaluate f'4.

Q: 18. Sőt dx √1-x²

A:

Q: Maximizing Profits The quantity demanded each month of the Walter Serkin recording of Beethoven's…

A:

Q: Find all rational zeros of the polynomial P(x) = 3x¹ - 3x³ - 7x²+x+2, and then find the irrational…

A: Given: px=3x4-3x3-7x2 +x +2 To find: Rational and irrational zeros of p(x)

Q: Find the limit by rewriting the fraction first. xy-y-3x +3 X-1 lim (x,y) →(1,5) x #1 lim (x,y)…

A:

Q: Evaluate the improper integral. √-3² O-49 07 0-7 49 dx

A:

Q: For the following vector field, compute (a) the circulation on and (b) the outward flux across the…

A:

Q: 4 6y' – 2y = xy¹, y (0) = -1

A: The given differential equation is: 6y'-2y=xy4        ......1  Initial condition y0=-1

Q: Consider the following position function. Find (a) the velocity and the speed of the object and (b)…

A:

Q: The rate of change in value V'(t) of a commodities index per day is given by the following equation…

A:

Q: Find the derivative of the following by increment Method 1. f(x) = 3X + 3 2. g(x) = 3x² - 4x + 4 3.…

A: As per increment method derivative of a function y=f(x) is calculated using…

Q: Question 4 > A trough full of water is 10 meters long, 1.5 meters wide at the top and 4 meters deep,…

A:

Q: EC1: Find a member of the family of solutions of ry"+y+√ = 0whose graph is tangent to the x axis at…

A: Solution: Consider  Substituting  gives,

Q: Find the two places on the curve y = x¹/³ - 8x²/3 x4/3 Y where the tangent is horizontal. (a) The…

A:

Q: Consider the following. -x³ + 4, -x² + 4x, Find the critical numbers. (Hint: Check for…

A: We have to solve following sub parts.

Q: Find the volume of the solid obtained by rotating the region bounded by the given specified axis. 6…

A:

Q: 1) y(x) = x, y₂(x) = z lnx, and y(x) = z² are solutions to a third order differential equation.…

A:

Q: 104d² 3d² + 7 A company that makes bicycles has determined that a new employee can assemble M(d),…

A:

Q: Set up the working equation in finding the area of the plane region bounded by y = -x² and x = -y²…

A: To set up the working equation in finding the area of the plane region  bounded by y=-12x2 and…

Q: Given the function f(x) = −2x² Find the difference quotient f(x+h)-f(x) h Find f'(x) by determining…

A: Please see the below picture for detailed solution.

Q: Model the data using an exponential function f(x) = Abx. f(x) = x 1 f(x) -51 X 2 -65.025

A:

Q: Evaluate the following summations. (a) _ Σ = 4k2 + 5k – 3 n-1 k=1 (b) Σ+1 i=1 Σ=&ij

A:

Q: Consider the region R enclosed by all of the curves y sin z, y = cos z, z = π/2, and z= . Which of…

A: Find the volume of solid

Q: x(t) Find the point at which the line y(t) z(t) = = -4-3t -8-5t intersects the xy plane. 4 - 6t

A:

Q: Consider the circle drawn in the xy-plane with center point (-5, 12). (x,y) (a) Determine the radius…

A:

Q: Maximizing the Volume of a Box A box with an open top is to be constructed from a square piece of…

A: Four square pieces at the corners of a square cardboard of size 12 × 12 Inches  And it was made into…

Q: Evaluate the definite integral by expressing it in terms of u and evaluating the resulting integral…

A:

Q: Find the acute angle (in degrees) between the planes x + 3y - 5z = - 6 and 2x + y 4z = 9. Question…

A:

Q: Find (s−1)′(−13) using the Inverse Function Theorem, given that s(x)=(−3x−1)/(−2x+9). Note that…

A:

Q: Determine convergence or divergence by any method. (-1)"n √n² +6 Σ n=0 The series diverges, since…

A:

Q: A cylinder is inscribed in a right circular cone of height 3 feet and radius (at the base) equal to…

A:

Q: A cylinder shaped can needs to be constructed to hold 550 cubic centimeters of soup. The material…

A: We have to find out the dimensions of the cylinder for which the cost is minimum.

Q: Find a function f(x) such that f'(x) = 7e² + 4x and f(0) = −2 f(x) =

A: We need to find out the function.