4.a) Is the equation Exact? * (y2 – 2xy + 6x)dx + (-x² + 2xy – 2)dy = 0 O Yes, the equation is exact. O No, the equation is not exact.

Q: g(z) h(2) If f(z) = then f'1) -

A: Given that:f(x)=g(x)h(x)                        

Q: EVALUATE THE INTEGRAL OF THE FOLLOWING. INDEFINITE INTEGRALS. CLEAR

A: We will find the integral's value. 

Q: XV In(5x) We substitute u = In(5x

A:

Q: )e*dx e2x +1 cot 3.

A:

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: Determine the derivative of y (x) = ( 3 x² + 11 x + 4 )³ e-6 x with respect to x. y '(x) =

A: topic - derivative of a function

Q: On the graph of f(x) = csc x and the interval (0, 27), for what value of x does f(x) = –1? Choose al...

A: Topic:- trigonometry  

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: Find the orthogonal trajectories of the given family of line y = Ce-mx with m held fixed. %3D

A: Given: y=Ce-mx

Q: Use a quick approximation to estimate the derivative of the given function at the indicated point. H...

A: We know that d/dx(xn)=nxn-1

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

A:

Q: Solve using homogeneous differential equation x*dy+(2.xy – y² kdx = 0 Let the substitution y=2; y=vx...

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: ydx = x + Vy² – x² dy

A: Given that: ydx=x+y2-x2dy

Q: Consider the graph of f(x) given below. (a) Analyzing the graph, if g(x) = f(æ), then g(x) is increa...

A:

Q: y=2C1cos(2x)+C2sin(2x), Eliminate Arbitrary Constant

A:

Q: Agree. Disagree 5. If lim f(x) # lim f(x), then lim f(x) does not exist. Justify:

A: Let's find. 

Q: How do you evaluate csc^-1(sec2)? It's an inverse function

A: We have to find the value

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

A:

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

A:

Q: tant dt. 1+ t2 F(x) = 1-2т

A:

Q: Edgar the engineer uses many complicated equations in his work. Before doing lengthy and time consum...

A: Hey, since there are multiple subparts posted, we will answer the first subpart as in b it asks to r...

Q: x^2y=4+Cy Eliminate Arbitrary Constant

A:

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

A:

Q: 3sin4t di 5(1– 3cos21)

A: To solve the integration. 

Q: Consider the series > 5e". n=0 a. The general formula for the sum of the first n terms is Sn (5e( 1-...

A: This is a problem related to series calculation. Based on the simplified terms it was observed that ...

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

A:

Q: Find the Taylor polynomial T,(x) and compute the error |f(x) – T2(x)| for the given values of a and ...

A:

Q: Evaluate whether the following initial values is true in the function: y=4cos(x/2)+3x² a.) when x = ...

A:

Q: If f' (2) = -5 and g'(2) = 3, find %3D (a) h'(2), if h(x) = 12f(x) + 4. %3D h' (2) = (b) F'(2), if F...

A:

Q: 1. Estimate the limit of the signum function s(x) as x approaches zero from the right. (-1, x0

A:

Q: x^3 + 3x^2 – 1 = 0, [-3, -2] Use the Fixed-point iteration method and Bisection Method  to find solu...

A:

Q: onsider the ellipse E in the xy-plane defined by the equation ax2 + y2 = 1 where a is positive. (1)...

A:

Q: 2. x'dy+(2xy-y'dr = 0 Let the substitution y=2; y= vx, dy=vdx+ xdv

A: x2dy+2xy-y2dx=0

Q: Find the exact length of the curve. 36y? = (x2 – 4)3, 4 0 23.335

A:

Q: f (x) = 2x? + 10, g(x) = 4x + 16

A: Topic:- geometry

Q: Solve the homogenous equation. 2. x*dy+(2.xy– y² kdx = Let the substitution v=: ²; y=x; dy=vdx+ xdv ...

A:

Q: Below is the graph of y = x +5. 20- 15 10- -4 -3 -2 -1 0 1 The area bounded by y = x +5 and the raxi...

A: Given problem:- Find The area bounded by y= x2 +5 and the x-axis from  x=-3 to x = -1

Q: Let f be a differentiable function. If f(50) = 378 and f'(50) = 6, use a linear approximation to est...

A:

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

A:

Q: Prove the identity 1÷(1-sinx) =sec^2 x +tanx secx

A: 1(1-sinx)=sec2x+tanxsecx

Q: Compute the resulting error in the function f (x) = x³ for value x = 2.38 with an error Ax = 0.005.

A:

Q: What is the equation of the directrix of the parabola X+2x+4y-27=0 2

A:

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

A: To evaluate the integral.

Q: Find the Laplace Transform of the given function. Show your solution completely and box your final a...

A: Given that: f(t)=t2sin2t

Q: Rewrite the statement in mathematical notation. (Let n be the number of cases of Bangkok flu and t b...

A: Given that - There are currently 200 cases of Bangkok flu, and the number is growing by 20 new cases...

Q: Center of Mass: Thin plate (region in the plane). Suppose Ris the region bounded by the graph of f(z...

A: Given:     f(x) = 4√x    Interval: [ 0 , 16 ] 

Q: The augmented matrix of a linear system has been reduced by row operations to the form shown. Contin...

A: topic - solution of linear equations using matrices

Q: What is the differential equation of the family of lines whose sum of the intercepts is fixed as k ?...

A: Given:  What is the differential equation of the family of lines whose sum of the intercepts is fixe...

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

A: