17) Water is falling on a surface, wetting a circular area that is expanding at a rate of 5 mm²/s. How fast is the radius of the wetted area expanding when the radius is 144 mm? (Round your answer to four decimal places.) A) 0.0055 mm/s B) 0.0111 mm/s C) 0.0347 mm/s D) 180.9556 mm/s

Q: Describe the graph of the equation. r = 18 cos ti + 4 sin tj -k O Itis an ellipse in the x = -1…

A: Let's find.

Q: If D is the region in the third quadrant between x +y? = 1 and x2 + y? = 4, then using the polar…

A: We have to convert given double integration into polar coordinates integration.

Q: 8:44 C ing e Determine whether the series is convergent or divergent. 00 1 n = 1 The series is a…

A:

Q: x² +64 Using trigonometric substitution, given - dx, the simplified form of the integral is: sec ede…

A: ∫x2+64x2 dxput x=8tanθdifferentiate on both siddx=8sec2θ dθ

Q: dy Find given x' +y =8.y. dx Note: Enclose all terms in a parenthesis if either the numerator or…

A: Topic = Derivative

Q: 9 – 4.x² -dx Evaluate: 9 – 4.x² – 2 sin () +C A f (x) = - B /9 – 4.x² + 2x sin- () +C f (x) = f (x)…

A: ∫9-4x2x2dx

Q: If f(x) = (x+1)/(x-1), where x # 1, determine f '(1). %3D

A: derivative of fx=x+1x-1 at x=1

Q: 1. The graph of a function y = a/b(x-h)+k shown below. -1 -40 Algebralcally determine two different…

A:

Q: S tan³ x sec x dx sec3 x - sec x + С none of the choices sec³ x + sec x +C 1 sec3 x + sec x +с В

A:

Q: Question 11 a / f(x) dx: f(x) dx a True False Question 12 If f'(a) = 0, then the function f must…

A: Here we have to use the concept of integration and derivatives.

Q: Jse the vectorized Euler method with h = 0.25 to find an approximation for the solution to the given…

A:

Q: dz In Vz+4 - 2 2ydy , if we let y=Vz+4, then the new integral becomes у-2 A True B False

A:

Q: 4. Find an equation of the tangent plane to the surface x = u? + 1,y = v³ + 1,z = u + v at the point…

A:

Q: 1. Use a parametrization to express the area of the given surface as a double integral and then…

A:

Q: If D is the region enclosed by y = , x = -3, and y= 0, then: II.-96y° dA =1. Select one: O True O…

A: Given problem:-

Q: y" + 4y" + 4y' = 0. %3D

A: Follow the procedure given below.

Q: Question 6 The tangent to the curve y = 1/x intersects the r-axis at (v2,0). What is its…

A: The tangent to the curve y=1x, intersects the x‐axis at 2, 0.To determine its y‐intercept.

Q: Qel Find the limis hth G8h alie んう0 2lim 土 2x2_8

A:

Q: Find the derivative of f(x) = 33x-1 O 33x-2 In3 O 33x-1 In3 33x In3 32x In3

A: (1). Given: fx=33x-1   As we know that; The Power law; ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

Q: Find T(t) and N(t) at the given point. r(t) = 4 cos(t)i +4 sin(t)j+tk; t= NG) - ||

A:

Q: What is wrong with this calculation? 1 dx = In 1- In 1 = 0 %3D Choose the correct answer below. 1. O…

A: Given expression is                                         ∫-11 dxx = ln x-11 = ln 1 -ln 1 =0    We…

Q: 4" converges or diverges. (7n)2 Use the ratio test to determine whether n=6 (a) Find the ratio of…

A:

Q: d d. Calculate ri(t) · r2(t)] and [ri(t) x r2(t)] first by differentiating dt dt the product…

A:

Q: x = 2y X=y-8 -12 12 -8-

A:

Q: Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints…

A: Solving

Q: S cot®x csc°x dx Gcot'x -cot"x + cot":) + c B none of the choices Gcot"x - cot "x - cot":) + c…

A:

Q: Evaluate the triple integral xyz dV, R where R = {(x, y, z)| 0 < x < 3, -2 < y < 1, 1 < z < 3}.

A:

Q: If t = x + ex, find d2x/dt2 given dx/dt = 1 / 1+ex.

A: dcdt=0 , where , 'c' is any constant. dexdt=ex .dxdt

Q: Describe the graph of the equation. r = 9cos ti – 19sin t j + k O An ellipse in the plane z = 1,…

A:

Q: each of the problems, solve the given differential equation. 1. y` = x2/y

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Sketch the region of integration and change the order of integration for the integral .3 A f(z,1)…

A: Given problem:-

Q: The figure shows the total number of cellular phone subscribers in a country from 2000 to 2008. niha…

A:

Q: 2X + Y+ 6z= 9 8X + 3Y + 2Z= 13 X + 5Y + Z= 7 X=2 Y=4 Z=15 O X-1 Y=1 Z=1 O X=1 Y=2 Z=1 O X=4 Y=2 Z=-7…

A:

Q: find S- とx 1-COS2X

A:

Q: Find:  ∫sin(3x) cos(6x) dx.

A: cos(2u) =2cos2u -1

Q: Find the values of a and b for the curve x*y+ay =b if the point (1,1) is on its graph and the…

A: Given,            The curve is x2y+ay2=b if the point 1,1 is on its graph and the tangent line…

Q: Question 8 x2 + 64 Using trigonometric substitution, given - dx, the simplified form of the integral…

A:

Q: Question 1 Which of the following are subspaces of R ? Choose all correct answers. {(x, y, z) E R³ |…

A: Only option 1 and 3 are subspace of R^3

Q: Question 1 half of the circle x +y? = 9. Sketch D, and give D in the polar coordinates. Evaluate the…

A: We will evaluate this double integral using polar coordinates.

Q: dy Given 4x -9y =1. Find by implicit differentiation. dx

A: Given 4x2-9y2=1 To find dydx

Q: Eind the limits lim hth G h Sinshe-Go

A: We have to find the limit according to the given information

Q: Give the parametric equation of the line that passes through the point (−4, 3, −5) and is…

A:

Q: nd derivative of f(x) = x In(x)

A: We have to find the second derivative of the given function

Q: If f(x) = (2x) , find the derivative of the function Or) = f'(x) = 3(x)0.5 f'(x) = -(x)0.5 f'(x) =…

A: 1)f(x)=(2x) -0.5 2)f(x)=(1+sinx)/(x+cosx).

Q: dy Find if yJx-9 =Xyt2 %3D

A: we have to find dy/dx

Q: UsinG PYTHAGORE AN IDENTITY, SOLVE FOR [sin Gx) - cos (Vx)] - 3x5 COS

A: The integration of the integral is  [sinx1/3-cosx1/3]2/(3x2/3).

Q: Type your answers in the following order and format: a=1,b=2. DO NOT include spaces in between…

A:

Q: S sec°x tan x dx +C + C sec³x + C

A: ∫sec5x tanx dx=∫sec4x (secx tanx) dxusing formula∫fn(x) f'(x) dx=fn+1(x)n+1 +cHere , f(x)=sec4x ,…

Q: dy Find given x' +y =8y. dx

A: Given  x3 + y3 = 8xy

Q: Q3 Find y ン ニ月(^)→ t(メッ) tanx 2 y-(1+x)

A: