The volume of oil in an inverted conical basin is increasing at a rate of 3 cubic inches per second. The height of the cone is 20 inches and its radius is 2 inches. At what rate is the height of the oil changing when the oil is 15 inches high? 0 02 th

Q: The radius of a circular disk is measured as 24 cm with a maximum error of 0.2 cm. By the…

A: The radius of a circular disk is measured as 24cm with a maximum error of 0.2 cm.

Q: Apply Newton's Method to f(x) and initial guess xo to calculate x₁, x2, x3. f(x) = x³ - 19, xo = 3…

A:

Q: Find a point on the ellipsoid x² + 4y² + z² = 30 where the tangent plane is perpendicular to the…

A:

Q: Integrate O √25 - 2² 2 ▶ X 25 - x² O. + C V6-ਏ 25 - x² 2 dx. +C 25 - x² + C 25 - x² + C

A: topic- indefinite integral ∫xn dx=xn+1n+1+C

Q: Find the determinate by expanding about the 1st row. 1 3-1 223 1-1 0

A:

Q: integral of cos x sin^3 2 x dx

A:

Q: Consider the indefinite integral fe5z +6 dæ: a) This can be transformed into a basic integral by…

A:

Q: Part b: (**) We consider the function f(x, y) = x sin y - y cos x + X-R y Find fx(x, y), fxy(x, y),…

A:

Q: Use the Comparison Test or the Limit Comparison Test to determine whether the following series…

A: We need to choose correct option.

Q: Let f(x) = x² - 5x. (A) Find the slope of the secant line joining (3, ƒ(3)) and (9, ƒ(9)). Slope of…

A:

Q: Consider - 2x 2) (² f(x, y) = e fxx + fyy = 0 cos 2y - e -2y cos 2x. Verify that

A:

Q: Integrate fx Sx O cos(4x) dx (sin(4x) - x sin(4x)) + C cos(4x) + 4x sin(4x) + С (4x sin(4x) +…

A:

Q: Set up the definite integral required to find the area of the region between the graph of y = 13-²…

A:

Q: Choose the normal vector of the tangent plane to the surface defined by at the point (-4, 2, e88). O…

A: Given problem:- Find the normal vector of the tangent plane to the surface defined by…

Q: Use the given information to find the exact value of the trigonometric function.  sin θ = 1/4 , tan…

A:

Q: Integrate da - z Select one: O A. In | ¹²² | + √1 - ² + C --- I OB. 2in1 - 2in1-¹² + √1-x² + C OC.…

A:

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: This question can be solved using the concept of the stated theorem 13.9

Q: The angle of elevation of the Sun is 35.3° at the instant the shadow cast by an obelisk is 741 feet…

A: The given angle of elevation of the Sun is 35.3° at the instant the shadowcast by an obelisk is 741…

Q: IntegrateIn(a) da. о х5 5 x5 ln(x) - x5 25 x5 In(x) - - 25 x4 5 ·ln(x) + 1 X - x5 5 x5 25 +C + C + C…

A:

Q: Solve the initial value problem: y'(x)=√-2y(x) + 35, y(-2) = 5

A:

Q: Let F(x) = = (x − 3)³ − 4 cos (x-3) Find lim F(x). x 3 + lim F(x) = x+3+ x < 3 3 ≤ x

A:

Q: Use Linear Approximation to estimate Af = f (7.01) - f(7) for f(x) = x². (Use decimal notation. Give…

A:

Q: In reference to the following function:  f (θ) = (θ − 3) cos(θ) Write down an expression,…

A: use the polar curve to find the expression of the area.

Q: Choose the gradient of the function f defined by f(x, y, z)= In[1 + (17xy + xz +9yz)²].…

A:

Q: = Which of the following represents the shaded area between y J(a) and y = g(x)! 8 6 2

A: We are asked to find which is represented for shaded area between the curves

Q: Suppose that we know the following about functions f(x) and g(x). 5 f(x) dx = 4; ₁ 5 S.. Use this…

A:

Q: Use the Integral Test to determine whether the following series converges after showing that the…

A: If f(x)  is a continuous, positive and decreasing function on the interval [k,∞)  and  f(n)=an…

Q: A university is trying to determine what price to charge for tickets to football games. At a price…

A: We need to find price and no. of people.

Q: Sy²sin (2y) dy

A: Integration by parts.

Q: Use the given information to find the exact value of the expression.  cos θ = 5/13 , θ lies in…

A: Given :cosθ=513

Q: The differential equation Find such a solution and then give the related functions requested. dy =…

A:

Q: Consider the accumulation function A(z) = Calculate A(5) Question Help: Video -1² (4t +9)dt Submit…

A: This question is related to definite integration, we will solve it using given information.

Q: 6. Use the definition of Maclaurin series to find the first four nonzero terms of the Maclaurin…

A:

Q: Estimate Ay using differentials. 1/33x-1, y = x ¹/3 e³x-1. a = 1, dx = 0.1

A:

Q: Alice is staying in a cottage along a beautiful and straight shoreline. A point on the shoreline is…

A: We have to find minimum time in hours.

Q: Solve the following initial value problem: y(t) = = dy dt +0.9ty = 6t, y(0) = 1

A: Given: dydt+0.9ty=6t,      y0=1

Q: Work Problems ( your works 1) Let F(t)=(4t — t²)i+t² j+sin(5t — 10) k a) ... :) Find the unit…

A:

Q: Use the Limit Comparison Test to determine convergence or divergence. O 8 Σ n=1 O Select the…

A:

Q: Use the formula for the general term (the nth term) of a geometric sequence to find the indicated…

A: We have to find the 10th term. The general term geometric progression is given by- an=a1rn-1

Q: 1. dx x³ + x²

A: Given, ∫1x3+x2dx

Q: The partial derivative fx(-1,0) of ƒ(x, y) = xe³ + x² + 1 is equal to −1. Select one: True False

A:

Q: lim, 0 tan² (7x) cot(11x) (r+7)sinx

A:

Q: a) Find an equation of the tangent plane to the surface at the given point. xyz = 15, (1, 3, 5) b)…

A:

Q: Use an appropriate test to determine whether the series converges. Σ k=1 By the 9 k 12 9 this series

A: Please see the below picture for detailed solution.

Q: For a given cylindrical tank, the radius is 2m and the height is 18m. The tank is filled to a depth…

A:

Q: S cscycoty 1+cacy dy Select one: OA. - In (1+ csc y) + C OB. In (1+ csc y) + C OC. In² (1+ csc y) +…

A: Given problem:-

Q: Compute the determinant of the matrix by cofactor expansion. 325 114 O-56 -8 O110 8

A:

Q: Question 22 A square is increasing in area at a rate of 20 mm² each second. Calculate the rate of…

A:

Q: Find the directional derivative g(x, y) = x² + y², of the function at P in the direction of v. P(5,…

A:

Q: Consider the function f(x)=5x2−9x7f Let F(x)F be the antiderivative of f(x)with F(1)=0 then f(x)

A: we have to find the function F(x) .