The formula for the volume of a cone is given below. Find the rate of change of the volume for each of the radii given below if dr/dt is 6 inches per minute and h = 27r. V = (1/3)лr²h (a) r = 4 in V = (b) r = 15 in V = in³/min. in3/min.

Q: Answer true or false. If f is not plecewise continuous on [0, 00>), then {f(t)} will not exist. O…

A: Note that, L{f(t)}=F(s)=∫0∞e-stf(t) dt...(1)

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

A:

Q: Using the given graph of the function f, find the following (a) the intercepts, if any (b) its…

A: Given graph:-   To find:- Using the given graph of the function f, find the following(a) the…

Q: Q1: Solve Ine+4-210x=logo 100 for x a) x=1 b)x=0 c)x=(1,-1) 07 If (()=x² (2 Inx-3) Find f'(x)

A: Solve lne+4-2log4x=1xlog10100 solve for x

Q: 11 sin (0) cos³ (0) + 3 cos (0) do

A: Our Aim is to evaluate the integral given below:-∫11 sin θcos3 θ+3 cos θdθ -(i)

Q: a) xin x-x Q3. If f(x)=x+2e b) 2 b) 4xln x-4x then find ¹)'(2)= c)-2 b) 2 d) 1

A:

Q: Let s(t) v(t) = 6t³+9t²360t be the equation of motion for a particle. Find a function for the…

A:

Q: Determine which function is a solution to the differential equation xy' + 3y = 0. 3x

A:

Q: Determine the height h above the base of the centroid of the cross-sectional area of the beam.…

A:

Q: 3. A child holds a ball 4 feet above the ground and throws it. The ball follows a parabolic path…

A:

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = xªcos x, n = 2, C = T

A:

Q: Given the ellipse 9x² + 16y²-144 = 0 a) determine the length of arc in the first quadrant.  b)…

A: Given region in the first octant bounded by  xy=1 , xy=3 , y=2x and bounded below z= 4 i.e z=0 to z=…

Q: A first order differential equation involving current i in a series R-L circuit is given by: di/dt…

A: Laplace transform

Q: Problem 3: Find the value or values of c that satisfy the equation the mean value theorem for…

A: To find the value or values of c that the equation fb-fab-a=f'c in the conclusion of the mean value…

Q: Find the directional derivative of the function at P in the direction of v f(x,y,z xy + yz + xz,…

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: Verify the identity. (Simplify at each step.) 2 cos² B - 2 sin² ß = 2-4 sin² B 2 cos² B-2 sin² B =…

A: The given identity, 2cos2β-2sin2β=2-4sin2β

Q: The polar coordinates of a point are given. Find the rectangular coordinates of this point. 2π 3…

A:

Q: 2x+5x7 x3 1²2 dx

A: To evaluate the given integral.

Q: Find a differential equation whose general solution is y = C₁e6t + c₂e-4t y" - 2 y' - 24 = 0 X

A: The solution of the DE is: y=c1e6t+c2e-4t where the solutions to the auxiliary equation are 6 &…

Q: Find the arc length s of the curve y= x2 on the interval  [0,2]

A: The objective of the question is determine the arc length of the given function.

Q: 12. Find the directional derivative of f(x, y, z)=zy+yz+xzat (1, 1, 2) in the direction of u =…

A: We can find the directional derivative in the following steps.

Q: lim, 0 6 tan² (5x) 15x²

A:

Q: Find the absolute maxinum and minimum values of the function over the indicated interval, and…

A: Here, the given function is: f(x)=8x+3 which is a linear function. So, it has no critical point.…

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A:

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim_(ti + sin(t)j +…

A:

Q: 4. Verify that the y defined below satisfies the following boundary value problem. -x Sy" = 8(x -…

A: The Dirac delta function is defined such that ddxHx=δx, where Hx=1x>00x≤0is unit step function.…

Q: y'+y=e-6 cos St, y(0) = 0

A:

Q: Q12) If f(x)= In(-5+x), then the domain of f(x) is (a)x>0 (b) x 5

A:

Q: The region bounded by f(x) = - 2x² + 8x + 24, x = = 0, and y = the volume of the solid of…

A:

Q: HOW YOUR CALCULATIONS 2. Do the following directions lie parallel to the plann? [211] ||(111)

A: Do the following direction lie parallel to the plane? [2 -1 -1]||(1 1 1)

Q: Use the formula к(t) = = k(t) = = ||r' (t) × r"(t)|| ||r'(t)||³ r(t) = t²i+t¹5j to find (t).

A:

Q: Given compute the following integral. Provide your answer below: (f(x) + g(x)) dx = [ f(x) dx = 5…

A: Given that , ∫35fxdx=5 and ∫35gxdx=14 find ∫35fx+gxdx=?

Q: 0.6 T² 9 - 25x² dx

A: The given integral is x2/sqrt(9-25x2), limit from 0 to 0.6.

Q: d/dx(y(x)) if x and y are related by the parametric equations x = t+sint, y = t^t

A: Given  equations x = t+sint, y = t^t

Q: L{F(t))} = √° e-stf(t) dt to be the Laplace transform of f, provid [6, 0≤t<3 lo, t≥ 3 lete the…

A: Topic:- application of integration

Q: (c) f(t) = -7t-u{t-10}.

A:

Q: Question 14 A line is tangent to y = x³ - 2 at (2,6). What is the coefficient of x when the line is…

A:

Q: Find a degree 3 polynomial that has zeros -3, 2 and 5 and in which the coefficient of ² is - 12. The…

A:

Q: Question For the function f(x) = 5x + 2, it is given that f(x) f(x) dx = 102. At what value c does…

A: Here, note that the average value of the function in the interval [0,6] is given by: f=16-0∫06f(x)…

Q: Find dy/dx: y = √√√2x¹ + 3x² +5

A: I have stated the used formulas in the solution

Q: Consider the functions f, g, and h, which are differentiable for all x € R and h(x) − 2 #0 - for all…

A:

Q: - A gardener has 120 feet of fencing to fence in a rectangular garden. He wants one side of his…

A: According to the question: l+3w=120 or l=120-3w a)The area A of the garden is:           A=lw…

Q: For the function, do the following. f(x)=√x from a = 2 to b = 5. (a) Approximate the area under the…

A:

Q: Sketch the space curve. Vector-Valued Function r(t) = -ti + 2tj + 6tk O 5 5 5 * * kk 5 Z Find its…

A: We have to sketch the vector and find the length of curve.

Q: Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t > 0. Then…

A:

Q: Find the following for the given equation. r(t) = (e-¹, 3t², 6 tan(t)) (a) r(t) = (b) r(t): (c) Find…

A:

Q: Find the Laplace transform Y(s) = L{y} of the solution of the given initial value problem. Y(s) = y"…

A:

Q: Question Define as the region bounded by the functions u(y) = y² + 1 and v(y) = y between y = 1 and…

A:

Q: Σ 500(1.07)" ΕΞΟ

A:

Q: 3 (1 + 2x - 4x³) dx

A: The given integral is ∫131+2x-4x3dx