1. Water is being poured at the rate of 2 n m³/min. into an inverted conical tank that is 12-meter deep with a radius of 6 meters at the top. If the water level is rising at the rate of -m/min and there is a leak at the bottom of the tank, how fast is the water leaking when the water is 6-meter deep? (hint V= r²h)

Q: Find the polar eauation for the curve represented by the given Cartesian eavation. Dy=-4x² 1.

A: We need to find polar equation.

Q: Question You are stationary on the ground and are watching a bird fly horizontally towards you at a…

A:

Q: an = In(n+1) – In(n) for n E N determine if the following is convergent or divergent { an } n=1

A:

Q: 1 In solving the antiderivative of f(x) 2-3sin(x) by miscellaneous substitution, the substitution…

A: Given problem:-

Q: What is the general solution of the system x − 2y + z = 3 2x − 3y + z = 8   Multiple choice…

A:

Q: Let slx) = tan X %3D 3, ind ) tanx dx using Lebesgue in tegral.

A: To evaluate the integral.

Q: ) Solve the D.E dy + (xy – xy²)dx = 0

A:

Q: Given: S 10xe", 2а3 + За2 — 12а, х >0 x < 0 f(x) = + За? — 12х, х a. Find all the critical numbers…

A:

Q: Find the points on the curve y= (x-1)(x -4) where the tangent line is parallel to y= -4x, O (3, 10)…

A:

Q: 1. Mang Vicente has 1000m of fencing material and wishes to enclose a rectangular field. Two (2)…

A: Mang Vicente has 1000 m of fencing material and wishes to enclose a recangular field. Two adjacent…

Q: S (2x² + 3)dx S(5 +) dx 4.) 5.)

A:

Q: Q3) Evaluate triple integral dz dx dy.

A:

Q: From Rogawski ET 2e section 10.3, exercise 10. Use the Integral Test to determine whether the…

A: Given problem:-

Q: Find the volume of the following solid. The tetrahedron bounded by the coordinate planes (x-0, y= 0,…

A: Given problem:- Find the volume of the following solid.   The tetrahedron bounded by the…

Q: Solve if the improper integral below diverges or converges. If it converges, solve for the value. La…

A: This question can be solved using the concept of convergence and definite integrals.

Q: 5) S dy 5.)

A: The given integral,      ∫28-y2dy

Q: For the functionf(x) given below, evaluate lim f(x) and lim f(x). x00 X→ー0 f(x) = -5x - 3x + 2 cos…

A:

Q: an = In(n+1) – In(n) for n EN determine if the following is convergent or divergent { { an } n=1

A: If an=lnn+1-lnn for n∈N,then to determine whether the sequence, ann=1∞ is convergent or divergent.

Q: Determine whether the following series is convergent or divergent full solution pls and write what…

A: The given series,          ∑n=1∞3-n4n34

Q: Consider the integral 5 x (z° +1) dx. In the following, we will evaluate the integral using two…

A:

Q: -ions of the line through (-1, –2, 5)

A:

Q: Q2) Solve the D.E xdy + (2y – x* + 3x)dx = 0 %3D

A:

Q: п(х — 2)" 3" (2n – 1)3* VI. Consider the power series n=1 a. Show that the power series converges…

A:

Q: Compute f'(a) using f'(a) = lim f(a + h) – f(@) or f'(a) = lim Tx) – J(d) for f(x) = 15x³, a = 2. or…

A:

Q: Identify if the following series is convergent or divergent: 00 (-1)"3n² 4n2–1 n=1

A:

Q: Find an equation of the plane through (-7, 2, –6) that is perpendicular to the planes 4x – y + z = 4…

A:

Q: Solve for "z" 7x + 3y + 8z = 10 -8x + 1y - 5z = 18 1x - 8y + 2z = 16 Round answer to 2 decimal…

A:

Q: (x – y)dx + xdy = 0. (x – 2y)dr + xdy = 0. (x² – y?)dx + 2xrydy = 0.

A:

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A:

Q: (-1)" Given: power series (x + 1)" 2n2 + 5 i. Determine if the resulting series of constant terms…

A: We have to check whether the given series is convergent or divergent.

Q: Classify all the critical point(s) of f(x, y) = e(+). Find maximum and minimum value(s) of f(x, y).

A:

Q: O Fnd the pemainders when @ x³ - 2xx +5x +8 is divided by x-2, (b) x+ x -9 s OC +1 dwided by is…

A:

Q: 2. Sketch the plane curve by plotting points then indicate the orientation of the curve. x = t2 – 4…

A:

Q: Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not…

A:

Q: In(arctan(x)) dx 1 + x2 1

A:

Q: Solve ? d'N di? dN 2t- + 2N = t In t -- dt 1 Add file

A: Solve the following

Q: æP In(x) dz a. Find the values of p for which the integral converges. The integral converges for all…

A: ∫01 xplnxdxApplying integral by parts,=1p+1xp+1lnx01-∫01xpp+1dx=1p+1xp+1lnx-xp+1p+1201=-1p+12…

Q: A. LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS 5. (2D* – 3D3 - 2D²)y = 0

A: According to Bartleby guidelines I can only answer the first question of the given two questions.…

Q: Use the limit definition to compute the derivative of the function f(x) = Vx + 2 at x = 1. (Use…

A:

Q: x²y(cos(Tz) +2) dæ dy dz

A:

Q: PART II. Find the derivatives of the following expression, solution must be presented. 1. x²y – ỹ =…

A:

Q: Ssec*x (Vtan²x + 1) 2. 4 sec' x tan3, dx

A:

Q: Find an equation of the plane that passes through the points (1,5, 2), (3, 4, –2), and (-–5, 5, 1).…

A:

Q: LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS 1. (9Dª + 6D³ + D²)y = 0 2. (4Dª – 45D² – 70D – 24)y = 0

A:

Q: Q5) Find volume of body bounded by z = 0 from below and z = 4-x from above inside x = y2 ,x = 4.

A:

Q: xist enter DNE.

A:

Q: Determine if the improper integral converges or diverges. Find its value if it converges. Show…

A:

Q: The antiderivative of [Vx-25 dx is V x2 - 25 - sec-x+ C. A True B False

A: Given: I=∫x2-25xdx     As we know from the trigonometric identities; 1). sec2x=tan2x+1 2).…

Q: Each of the regions A, B, and C enclosed by the graph of f and the x-axis has area 6. Find the value…

A: Answer and explanation is given below...

Q: Find f"(1) if Ax) = X+1. %3D 1 1 1/4 12 OOO

A: To find f'1 if fx=xx+1.