dx 4. Evaluate the integral by trigonometric substitution: , Væ²-9

Q: Let T3 be the Maclaurin polynomial of f(x) = e*. Use the Error Bound to find the maximum possible va...

A:

Q: Find an equation of the tangent line to the curve 2(x² + y)² = 25(x² – y²) (a lemniscate) at the poi...

A: Given that 2x2+y22=25x2-y2To find : equation of tangent line at point 3,1Solution :2x2+y22=25x2-y22×...

Q: (x) = x^2 +3x-4, which of the following represents the solution for the equation?

A: Topic:- algebra

Q: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

A: The given function is: f(x,y)=(x2+2y)e2xy+8xy...(1) The function f(x,y) is said to be homogeneous fu...

Q: zetch the region(s) enclosed by the given curves. Find the area oft y = r and y = VI 11

A:

Q: f (t) = 7e – 2t sin(3t)

A:

Q: Calculating Mass from Linear Density. Mass-Density Formula of a One-Dimensional Object. Given a thin...

A: Topic:- application of integration

Q: Evaluate the definite integrals using the graph of f (x) below. 4- y 2- 2 10 12 -2- -6 (a) Number (b...

A:

Q: dy (а) Find for y = cosh(4x). dx 10 (b) Find ( + i) 4

A: Given that: (a)y=cosh(4x)(b)14+14i10

Q: y = Vx (x – 1) u = i + ī + 4/15 y = f (r² + t + t')

A:

Q: What is the differential equation of the family of ellipses with their centers origin and their majo...

A: Let us solve the problem using the basic equation of ellipse  later we will use different methods to...

Q: 1 I. Evaluate dV, where E lies between the spheres x? + y² + z² = 1 and x2 + y? + z² E x2 + y? + z? ...

A:

Q: 1.Determine if the following statements are mathematical or not. Provide solution. a. Today is MMW c...

A: We know a mathematical statement is either true or false .

Q: Find the orthogonal trajectories of the family of ellipses with centers at (0, 0) and two vertices a...

A:

Q: 124 Х 209

A:

Q: 2e*dx where e = 2.7183 %3D

A: Given: I=∫012exdx   As we know from the integral; ∫a·fxdx=a·∫fxdx, where 'a' is the constant. And ∫e...

Q: Find the DE of each of the following by eliminating the arbitrary constants. y =Ce* +C2cos.x +C3sin ...

A: Herw we have to find the differential equation.

Q: 2. 3t2 (t3 + 4)5 dt 3. 5x2 1- х3аdx

A:

Q: 3. Solve the differential equation by variable separable method (1+ y") (3a² + 6) dy 9- dr 13 + 6r

A: dydx=91+y23x2+6x3+6x  

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

A: use some property of limits.

Q: Use the Integral Test to determine whether the infinite series is convergent. -n2 16пе n=6 Fill in t...

A: This is a question related to series and sequence calculation. For using integral test for given ser...

Q: All parts of this problem refer to the function below. y = (9+ 6x)²/¤ dy a) Use logarithmic differen...

A: We have to find derivative

Q: On the graph of f(x) answers that apply. = tan x and the interval -27, 0), for what value of x does ...

A:

Q: On the graph of f(x) = cot x and the interval 2T, 47), for what value of x does the graph cross the ...

A: Follow the procedure given below.

Q: A wound is healing in such a way that t days since Monday, the area of the wound has been decreasing...

A: We have to find area on Monday.

Q: Finding the length of a curve. Arc length for y = f(x). Let f(x) be a smooth function over the inter...

A:

Q: Calculating Mass from Radial Density. Mass-Density Formula of a Two-Dimensional Circular Object. Giv...

A: Given: m=∫0r2πxρxdx  ...(1) And ρx=6x ; x=6   We know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1 A...

Q: 1. y'dx-(xy + y dy = 0 Let the substitution v=2; y = vx; dy=vdx + xdv

A:

Q: The Center of Mass of a Thin Plate (region) Consider the region in the zy-plane bounded by the curve...

A:

Q: 8x sin x y" + 4y/ + 5y = 8x sin x 1. ollowing econd ifferential equation:

A: The given differential equation is:y''+4y'+5y=8xsinx

Q: Question 14 Which of the following is an equation of the parabola with the following properties: ver...

A:

Q: Agree. then lim f(x) does not exist. Disagree 3. If f(a) is undefined, Justify:

A: Given

Q: By using substitution method, evaluate: (a) dx (e3x+x3)3 (In x) dx (b) 4x

A: To evaluate the integral.

Q: 6x2 – z+1 1→7 2x2 + 3x - 1 Find the limit, if it exists: (Do not use L'Hospital's rule) lim Note: Gi...

A: limx→76x2-x+12x2+3x-1

Q: 69x420

A: Given query is to perform indicated multiplication operation.

Q: A wound is healing in such a way that t days since Monday, the area of the wound has been decreasing...

A: topic - application of derivatives

Q: Write an expression for the distance w in terms of y. Simplify your answer and write the terms in de...

A:

Q: y'dx-(xy + y* \dy = 0 1. Let the substitution v=²; y=vx; dy=vdx+ xdv

A:

Q: x- 1 (i) y = () y = Vx(Vx+1) x + 1

A:

Q: deteremine the solution of the following equations using the methods in solving for solutions of dif...

A: Differential equation problem   , v =  y/x   form 

Q: Set up and evaluate the integral that gives the volume of the solid generated by revolving the plane...

A:

Q: Obtain the Taylor series expansion of the function f(x) = cot x centered at a 4

A:

Q: Sketch the region bounded by the graphs of the equations and find the area of the region. y = cos x,...

A: The region is bounded by y=cos x and y=2-cos x, 0≤x≤2π

Q: -3 evaluate the integral (x2 – x + 2) dx using its definition.

A:

Q: x*dy+ (2xy – y³ ktx = 0 Let the substitution v=2; y= Vx; dy=vdx+ xdv

A: Topic:- differential equations

Q: 3. The function f(x, y)= 8x' - /4x° +3y° is homogenous in x and y of degree 4. The function f(x, y) ...

A:

Q: determine the most general function M(x, y) or N(x, y) so that equation is exact.

A: We have to find M(x, y) Or N(x, y). 

Q: x*dy+ (2.xy – y² }tx = 0 Let the substitution y=²; y=vx; dy=vdx+ xdv v = =

A:

Q: Find the volume generated by revolving the region above the curve y=x3 , under the line y=1, and bet...

A: Given: y=x3, y=1, x=0 & x=1 From the given curve the bounded region is as shown below: Apply th...

Q: Please solve and show all work. Thank you!

A: Topic:- geometry