Let y = √x . Then dx is:

Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = [*^f(x) dx + [²8(x) x +…

A:

Q: 3x The directional derivative of f(x,y,z)=ln 1+yz at the point P (2,0, -1) in the direction from P…

A:

Q: Which ONE of the following statements is FALSE? OA. If the function f (x,y) is maximum at the point…

A:

Q: Let y = = 1/2 √ √x. Then evx dy dx is:

A:

Q: Evaluate the following integrals (a) 2x+3x-2 dx

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

Q: Assume acceleration due to gravity is -32 ft/s². A ball is thrown vertically upwards from a platform…

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: The graph, when the curve y = √3 + x² from x = 0 to x = 4 is rotated about x - axis is A B C D

A: To find the graph of the solid formed by rotating the given curve about x axis, first we find the…

Q: The value of x for which the series Σ- O A. x<2 or 4<x. OB.2<x<3 or 3<x≤4. OC.2<x<4. O D. 2<x<3 or…

A: Given

Q: Evaluate the integral given below. Check your answer by differentiating- NOTE: Enter the exact…

A: To evaluate the integral given below. To check theanswer by differentiating.∫16t-6 et dt=?+C

Q: Find the equations of the tangent and normal to the curve √√√√y=1 at (9,4) a. Tangent: 3x - 2y = 3;…

A:

Q: 4. g(x) = (3x − 2)4; g"" (x)

A: We can find the derivatives as below

Q: Find the critical points of ƒ(x) = −6x² + 4x² − 9 and apply the Second Derivative Test (if possible)…

A: We have to find point of local maximum and local minimum for the given function.

Q: X 4e² Evaluate Sv dx 2 Use rationalizing substitution. A e√ex - 2 = 2√2 Arctan 1/2 √et et - 2 + C…

A: We have to find value of given Integral.

Q: - Given the function f(x, y, z) = x ln(1 – z) + and simplify your answers. a) fa b) sin(x - 1) 2y…

A:

Q: tex Given; ·S= dx 2 Applying rationalizing substitution, find dx in terms of z. (2 z + z) dz A z² z…

A:

Q: (4) Find Laplace Transform F(s) for the variable x or y in the equations a-y"+2y'-3y=32e"; y'(0) =…

A:

Q: Kindly make a sign table for the graph

A: Solve the following

Q: 4.Determine the area bounded above by y: 5 + x² and below by y = 1 + 2x²

A:

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

A:

Q: 4. The region is bounded by y = x³, y = 2x + 4 and y=-1. The x coordinate of the centroid of the…

A:

Q: Let f (a, b, c) = cos (ab) + sin (b) + c where f ¹ ((1/5,²)) af 1 T Evaluate да 23 π T√3 12 3 Option…

A: I am attaching image so that you understand each and every step.

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: anufacturing budgeted $60,000 per mont for lab rials. If $x is spent on labor and Sy is spent on…

A:

Q: Sketch the graph of the function f(x): = 2x-3 x²-4

A: The function is  f(x)=2x-3x2-4

Q: Find the volume of the solid obtained by rotating the region bounded by y = x + 1, y = 0), and X=2…

A:

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

A: Solve the following

Q: Question 10 The radius of convergence of the series (-1)" (n!) 0 3-6-9. (3n) Place) -(2x-1)" is…

A:

Q: Hnew ³ Let w=f(u) + 9 (v); where u = x+iy and V=X-iy, show that w satisfies the Laplace eap. Wxx +…

A:

Q: uestion 12 The power series representation of f (x) = ln(x2 – 1) is given by A. None of the choices…

A:

Q: The formula for solving for the area in the first quadrant bounded by y = x², the circle x² + y² =…

A:

Q: Which of the quantities is nearest to the value of * exp 0.003 1.001 cos(0.002) ? O 1 O 1.001 O…

A:

Q: indly provide a sign table with its conclusion of the curve sketching. (Concave up/ down, increasing…

A:

Q: 12

A:

Q: Find fy for the function f (x, y) = yx³ – 2x²y³ y - y³ x³ - 6x²y² Option 3 y - 6xy² 3 _ 2xy® -…

A: Topic:- application of derivatives

Q: Given that dy/dx = (x^2) and y=3 when x = -1, find the function f(x) in terms of x y-x+c--1 C

A: dydx=x23=x23

Q: of Let f (x, y) = tanh-¹(x-y) with x=e" and y= usinh (t). Then the value of dt (u,t) =(4, In 2) is…

A:

Q: If the function u = 2e^u e^2u 1/2 Other: In (2² +2²¹²) then ro + you is 4

A: First we calculate partial derivative.

Q: Find and classify all critical points of the function 3 f(x, y) = x³ + 2y - In(x³y³) Item 5.pdf

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: Find the volume of the solid generated by revolving the given plane area having the given boundaries…

A:

Q: f sin 3x cos 5x dx ¹29 sin 3x cos 5x + cos 3xsin 5x + C 16 sin 5xcos 5x + C O. 16 sin 3x cos 3x + O…

A:

Q: Consider a point in Cartesian coordinates given by (3√√/3, −3, −8). (a) Find a corresponding…

A: The given Cartesian coordinates are: (x,y,z)=(33,-3,-8) Now, the Cylindrical coordinates is given…

Q: 3x The directional derivative of f(x,y,z)=ln at the point P (2,0,-1) in the direction 1+yz z² from P…

A:

Q: Find O does not exist O-1/2 00 01 D 01/2 O Other e-1-1

A: We have to find the limit

Q: Find lim 2-0 -x-1 x²

A:

Q: W (4) Find Laplace Transform F(s) for the variable x or y in the equations a- +2y'-3y=32e³;…

A:

Q: The value of the integral in terms of u is? (a). 2u³ + 6u + Arctanu + C (c). 2u³-21n|u³+1| + C dx VI…

A:

Q: Set up the integral representing the area of the region between the curves = -1, x = 4, y = 2x - x²,…

A: