Equation Conversion from Polar to Rectangular Coordinates r² = x² + y² r cos 0 = x r sin 0 = y |× y tan 0

Q: Points A and B 1000 m apart are plotted on a straight highway running East and West. From A, the…

A:

Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 2x + 4y = 4,…

A:

Q: - Find the value of x of which the function f(x) = O a. none of these O b. 1 OC -1 O d. -3 Oe. 3 2-8…

A: Given:f(x)=12x-8

Q: fx,> 8 and x n+1 2 for n EN. Then the limit of x is equal to X 21 ......

A:

Q: 5 Given cos(8)= and the terminal side of 0 lies on the fourth quadrant. What is the value of cos 05…

A:

Q: Determine the area bounded by the curves x³ - y = 0 and y + 3x² - 4 = 0, using a vertical element. A…

A: Using vertical element form a double integral then solve it

Q: n! n=12n! +1 A. The limit does not exist. B. None of the choices in this list. C. The series…

A:

Q: A man drives 60 km North, then 45 km West. Finally, he drives 94 km South. How far away is he from…

A: The objective of the question is determine the distance and direction of starting and end point.

Q: The value of x for which the series - OA25x<3 or 3<x≤ 4. OBx<2 or 4<x. OC. None of the choices in…

A: We will solve this question by first calculating the radius of convergence of the series.

Q: Part II f(x)=x² A. g(x)=(x-3)² f(x)=x² B. g(x)=(x+3)² p(x)=(x-3)² +5 p(x) = (x+3)² +5 f(x)=x²…

A: We need to find vertex. As per Bartleby's guidelines we can solve only one part. Please upload other…

Q: Solve for the area of the region bounded by x² = 4y + 4 and x = y = 2

A:

Q: Consider the vector-valued function R(t) with Ả'(t) = (sec²(t − 1), - 2 Vt (a) Find R(t) given R(1)…

A:

Q: 2. The value of the integral in terms of u is? 2u³-21n|u³+1| + C 2u³-3u² +6u-6ln|u + 1| + C 6u+…

A: We know that integration of xn is xn+1/n+1.     Here i attached the solution of this question.

Q: S²S 1/2 The numerical value of 2e dxdy is equal to

A: Solve the following

Q: Find all critical points of f(x) = 1 + 10x - x² and use the First Derivative Test to determine…

A: We are given f(x) = 1+10x-x2 We have to find critical points of f(x) and using first derivative test…

Q: h-x'+2x=10e³ where x(0)=6

A:

Q: √√2₁ y = ¹, y-axis, y=1&y=3; OY

A: Volume of solid obtained by revolving region around y axis is evaluated.

Q: Evaluate Va²-x²dx using trigonometric substitution

A:

Q: Consider the series Σ(-1)^ 2³ Which ONE of the following statements is CORRECT? n=1 3" OA. The…

A:

Q: Find the derivative 4cos4t sin4t 2cot4t -1/2 cot4t Other: of the parametrically defined curve : x(t)…

A:

Q: The radius of convergence of the series Place) (-1)" (n!) 0 3-6-9. (3n) (2x-1)" is equal to…

A: To find the radius of convergence of the given series.

Q: Limzoo (√x² + 4x +1 − x) O a. 2 O b. none of these O c. -1 Od. -2 O e. 1

A: The objective of the question is evaluate the limit and choose the correct option.

Q: The integral can be rewritten as 6u³ (a). u + 1 6u4 (c). u² + 1 :). -du du dx 3³√x + √√x 派 派 6u² u²…

A:

Q: A force of 3.0 pounds is needed to stretch the spring to 1.0 ft. from its natural length of 10…

A: Given problem:- A force of 3.0 pounds is needed to stretch the spring to 1.0 ft. from its natural…

Q: Consider the region on the 1st quadrant bounded by y = √4x², x and y- axes. If the region is…

A: Using disc method, find value of a+b+f(1)

Q: If R is the disc with center at the origin and radius 5 then the numerical value of [xdA is equal to…

A: Please follow the next step.

Q: The graph of the area between the curves f(x) = x and g(x) = x^2 on interval [0,2] O. O X & Y in…

A:

Q: The value of x for which the series A. 2<x<3 or 3<x<4. B. x<2 or 4<x. C. 2<x<3 or 3<x ≤ 4. D. 2<x<4.…

A:

Q: Evaluate the given limit of the following: lim (et + t)¹/t t-0+

A:

Q: dy Find dif: y = ln(x + √² + a² O a √2+²+² O b. √ О с. √√2²+0² O d. none of these O e √√zta

A:

Q: 2. Using your calculator, determine how many solutions the system has. Then without a calculator,…

A: This question is based on solution of Polar function.

Q: 5 3 +-6-0 dx 4 dx 3 dx 2x - 3x a.y = (C₁ + C₂ + С₂)e* + С²e²x + С¸è¯ С_e 2 5 2 2x -3x b.y = C₁ + C₂x…

A: We have to find the solution of  d5y/dx5 +d4y/dx4 - 6d3y/dx3=0 This is a homogenous 5th order…

Q: 7. Evaluate * (D5 – 3D¹ + 8D³ + 16D² – 9D – 13)y = 0 y = (C₁+C₂x)e¯x + Сze* +C₁е²x cos3x +C5e²x…

A:

Q: anser

A:

Q: 12. y = 1 3t + 1³ X= 31² 1+1³ 3

A:

Q: Given the function f(x, y, z) = x ln(1 − z) + following and simplify your answers. a) | fx b) u fxz…

A: We can answer both the answer as below

Q: Write the parametric equations x = = 5 sin² 0, y = 3 cos² 0 e given Cartesian form. 3sqrt(1-x^2/25)…

A: Given query is to find the Cartesian equation.

Q: A piece of 1m wire is cut into two parts, one bent into the shape of a circle and the other into the…

A:

Q: The numerical value of the lim 818 n+3 nln (2) n+1 is equal to

A: We use L'Hôpital's rule to solve the limit.

Q: stion 12 The power series representation of f(x) = ln(x²-1) is given by OA. None of the choices in…

A:

Q: 13. Water is spilling out of a tank with a leak at the bottom. After t hours, there are t+ √t liters…

A:

Q: The volume for solid of revolution between curves is the volume of the object between a curve f(x)…

A: We have to find the volume.

Q: The numerical value of f3dA 3dA (where D is the region bounded by lines y=0 and x= 1 and the…

A:

Q: find dy/dx : y =3√tan3xx2

A:

Q: Consider the region on the 1st quadrant bounded by y = √4 - x², x and y- axes. If the region is…

A: Given problem:-

Q: y = (x²-2x) (In x³-3 tan x) x√x

A:

Q: 3. A rectangular plate is submerged in water as shown below. The top of the blue region is the…

A: Given

Q: Compute the partial derivative of the function * f(x, y, z)= el-roos(y) +2e=1/(1+²)

A:

Q: A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one…

A: We need to find equation.

Q: Determine the derivative of the following implicit function on a separate sheet of paper, assuming…

A: