2. √√√x + y + xy = 21

Q: Carbon extracted from an ancient skull combined only one-sixth as much as C14 as carbon extracted…

A: Let's find age of skull.

Q: 1. Find the volume of the solid generated when the region bounded by y = ex, x = 0, x = 2 and the…

A: Note: As per our guidelines we are instructed to solve only one problem. Hope you understand.    The…

Q: Evaluate the triple integral ryd xydV where E is the solid tetrahedon with vertices (0,0,0), (10, 0,…

A:

Q: [4pts] Consider a point in Cartesian coordinates given by (3√/3, -3, -8). a.) Find a corresponding…

A:

Q: 2) lim f(x) if f(x) = {x²43) X2² fx²-9, x2 x-2 F(x) X 2.75 2.5 2.1 2.01 2.001 X 1.5 1.75 1.9 1.99…

A:

Q: (CLO-2) The function f(x) = 2x³− 6x+4 decreases on 0 (-∞0,1) O (-∞, -1) U (1,∞) O (-1,1) 0 (-1,00)

A:

Q: A smooth vector-valued function R(t) satisfies R(1) = (-3,7,9), R'(1) = (0,5,6) and R'(1) = (4, 1,…

A: Explanation of the answer is as follows

Q: Consider the matrices shown below: Compute CT-A 3 07 A = -1 2 E -B C = 13] 3 1 5

A: Given: A=30-1211, C=142315

Q: hat are the cylindrical coordinates of the point whose spherical coordinates are

A:

Q: A retailer has been selling 1,000 computers a week at $750 each. The marketing department predicts…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: n = 3 20 . n=-1n+₂

A:

Q: A spherical tank of diameter 6 m is full of water. Find the work done in pumping all the content to…

A: Follow the procedure given below.

Q: Find the particular solution (D² + 4D + 4) y = 0 when x = 0, y = 1 and y' = -1 What is the general…

A:

Q: Use the Euler method to solve the following equation analytically for five iterations. Given that…

A:

Q: 2. Use geometry to evaluate (2 (2x+6)dx. You need to draw a graph.

A:

Q: Find 2 dr if y=1-t² and x= 4+² dx

A: 1.       dy/dt = d/dt [ 1- t²]   = -2t        2.      dx/dt  = d/dt [ 4t²]     = 8t   So now…

Q: Evaluate the triple integral a dV where E is the solid bounded by the paraboloid a = 10y² + 102² and…

A:

Q: The contact force therefore can be expressed as a a 27 F 2xÊ / ºr (d-1²) dr = -1°2xr 2xr Ozz dr n 2R…

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

Q: zl 5. Trigonometric form of the quotient of = 6cis (2); z2 = 2cis () is:

A:

Q: Consider the equations 2x - A) x² - 2x x³ +8 0 and B) = 0. x³ - 8 Which of the following statement…

A: We can find the answer in the following steps.

Q: Evaluate the characteristic w "+k²x ²³w = 0 value of k in the following differential equation w…

A:

Q: Directions: Assuming that the angles are in standard position. Determine whether the given pairs of…

A: If the difference of the two given angles is a multiple of 360° then the angles are co terminal…

Q: s-1 s(s+ 1)² -1+et+2te-t 2+te-t-e-t O Option 1 Option 3 1+et-2te-t Option 2 -2+tet + et O Option 4

A:

Q: 3. y²(x + 2y) = 8

A: The Solution is dydx=-y2(x+3y)

Q: The graph of a function y = f (x) is shown below. Use the graph to estimate all (there may be more…

A:

Q: Is f(x) = -3 A. Yes B. Does Not Exist continuous at x = 3? C. No D. Cannot be determined

A:

Q: -5e-cos2t O Option 4 5e-t sin 2t O Option 2 5e¹ cos2t O Option 3 5e sin 2t O Option 1

A: Topic:- application of derivatives and integration

Q: 1-12 Find the area of the surface. 1. The part of the plane x + 2y + 3z = 1 that lies inside the…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 4.3√√√7

A:

Q: What is the surface area of the solid generated by revolving about the y-axis, y = 1-², on the…

A: Given

Q: e critical points c for the function f and apply the Second Derivative Test (if possible) to…

A:

Q: 'ind R(t) given R(1) = (1,0,−1). 'ind f'(1) if f(t) = (-2, -3t, t²). R' (t).

A:

Q: Evaluate lim f(x), f(x) = (3x² + 5x − 1, (7x² - 2x - 3, x ≤ 2 x > 2

A: Topic:-  limit and continuity

Q: If f(x) = f*^²}} 2-1 5 1+1² dr. then what is f'(-3)?

A:

Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f near…

A: Use Taylor expansion

Q: Given the following set of data X 1 1.5 1.6 2.5 3.5 f(x) 0.6767 0.3734 0.3261 0.08422 0.01596 Find…

A: Solution of the problem as follows

Q: 4. Calculate the average value of each function over the given interval. Hint: use the identity sec²…

A: Average is evaluated.

Q: Find the critical points of f(x) = x³ - 21x² + 144x and use the Second Derivative Test (if possible)…

A: The given function fx=x3-21x2+144x

Q: X=2Seco y = 4 tano find cay dx² 1. when 0-1

A:

Q: [CLO-3] The second derivative f"(x) of a function is given. Use this information to determine where…

A:

Q: Find (au/ay), at the point (u,v)=(√2,-2), if x=u² + v² and y= uv. du (Simplify your answer.) ay…

A: Here we using jacobian formula.

Q: Obtain the output for t = 1.22, for the differential equation 2y"(t) + 27y(t) = et + et :y(0) = 0,…

A:

Q: 2. ff. x²y dy dx

A: Given

Q: Consider the following matrices: [2 3 id -1 27 - - A = B = 3 0 C = 1 0 b 4 1 Perform the following…

A:

Q: Use integration by parts to show that [x²³e³x² dx = 1 50 est (5x² −1)+c

A: ∫x3e5x2dxSubstitute u=x2→dudx=2x→dx=12xdu=12∫ue5uduIntegrate by parts:∫fg'=fg-∫f'gLet f=u and…

Q: 2. If x = 2a-3b-4c, ỷ = −2ã + 3b + 3c, and ž = 2ã − 3b-5c, determine the simplified expression for…

A: vector

Q: The proper way to evaluate f (3 + h) for the function f(x) = −4x² + 3x − 1 is Of(3+h)=(−4(3)² + 3(3)…

A: We can answer the question as below.

Q: Solve the DE by Integrating Factors Found by Inspection 3 1. x dy - y dx = x¹ y dy + x³y² dx X

A:

Q: Find the derivative of y with respect to x. y= (x8 Inx) 5

A:

Q: If A = 4x³ and (a) TRUE (b) FALSE dt dx 2, then dA dt = 150.

A: As we know the Power law; ddxxn=nxn-1 Given: A=4x3 and dtdx=2