v(e -Y cos x) • dr, where C is the line from (0,0) to (2x, kn 7)

Q: If f(x, y) = 4e*y cos (x- 1) , then the linear approximation at (1,0) is | (A) 4 + 16x (B) 4 + 4x…

A:

Q: If f(x,y,z)=xe^{4y}\sin(6z), then the gradient is

A:

Q: 24. Evaluate x² dx + yz dy + (y²/2) dz along the line segment C joining (0, 0, 0) to (0, 3, 4).

A:

Q: 8y'' - 12y' + 5y = 6 cos t

A:

Q: 2x :S dr f(x, y) dy. f (x, y) dy. •1-x² f (x, y) dy. -V1-r

A:

Q: If f(x, y, z) = ln(xª + yl0 + 2³) + V (x10 + y8 + z4), then find fr, fy and f; at (1, 1, 1).

A: The given function is fx, y, z=lnx4+y10+z8+x10+y8+z4 and the given point is (1, 1, 1). Evaluate fx…

Q: Compute DF(, ) of F(1, y) = (e" cos(ry), r² + y) %3D

A: Given function is F(x,y)=eycos(xy), x2+y Let  f1(x, y)=eycos(xy)f2(x, y)=x2+y

Q: Find fæ, fy, and fz. 4,5 f(x, y, 2) = 4z In (a*y° cos(5z))

A: We can answer all the three question as below.

Q: TRUE or FALSE: In the DE with linear coefficients (x – 2y + 4)dx – (3x – 6y + 9)dy, the associated…

A: The given ODE is: x-2y+4dx-(3x-6y+9)dy To check: of the coefficients associated to the DE are…

Q: integrate ​f(x,y)=x2−y over the curve​ C: x2+y2=4 in the first quadrant from (0,2) to 2,2.

A: The solution are next step

Q: Find d3f where f(x, y, z) = ln(x + y − z) + cos(x2y)

A: As per the question we are given a multivariate function as : f(x, y, z) = ln(x + y − z) + cos(x2y)…

Q: Q:1) Evaluate the line integral: [[xy'dx+x²ydy] C: [(x, y): x=t₁y=f²,0 ≤t≤1].

A:

Q: integrate ƒ over the given curve. ƒ(x, y) = x3>y, C: y = x2/2, 0 <=x<= 2.

A:

Q: obtain the particular solutions satisfying the indicated conditions: dx/y=(25-x^2)^-1/2dy; y(0)=1

A:

Q: 2) f(x, y) = x +y on the closed triangular plate bounded by the lines x 0, y= 0, y+2x = 2 in the…

A:

Q: I-x² f (x, y, 2) dz dy dx 1-x² Jo

A: we have to find the region of integration

Q: The student should estimate the equation 0.24 0.24 + tan [0.247 + 2(0.27)n] π 1 1 =-+-tan(Tx + 2ny)…

A: Given function: gx,y=xπ+xπtanπx+2πy Point: 14, 14 To estimate: 0.24π+0.24πtan0.24π+20.27π Formulas…

Q: Find u+ Hy:given that u(x,y) s tan(x+ux+ 11y") 11- x2-y?

A: The partial derivative of a multivariable function with respect to a variable is the derivative of a…

Q: 2.Find the particular solution of y (9x-2y) dx -x (6x-y) dy=0., when x=1, y=1. Let x=vy

A: Find out the particular solution.

Q: Evaluate . y? cos(x) dx + 2ysin(x)dy where C is the straight line between (0,0) and

A: The equations of the straight line joining (0,0)to π2,1 are x-0π/2-0=y-01-0=t(say) i.e. xπ/2=y1=t…

Q: What is the value of the line integral ∫ AB y dx + x dy, if x = 3*t, y = 4*t + 4 and 0 ≤ t ≤ 1?

A: I am solving this in step 2

Q: when (x, y, z) = (2, 2, 1). dt dz dy If x2 + y2 + z2 = 9, dx 8, and dt 4, find dt %3D %3D %3D dz dt

A: differentiate the given function with respect to 't' 2x dx/dt +2y dy/dt +2z dz/dt =0 Now substitute…

Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

A:

Q: |dx + N(x,y)dy = 0 x² + y,

A:

Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

A:

Q: evaluate the integral over this curve

A: This question is taken from the vector calculus in which we have to find the line integral of the…

Q: 30. Find an equation for the tangent plane to z = f(x, y) at (3, -2) if the differential at (3, -2)…

A:

Q: = (b) ſ sin (7(x – 2y)²) dA, where T is the triangle bounded by x – 2y T 1, y = −3x and 5y = -x.

A:

Q: Q) Compute for y(x) sec (2x) + 2x -1 and x(t) = 4cos(t) at t-1

A:

Q: integrate ƒ over the given curve. ƒ(x, y) = x + y, C: x2 + y2 = 4 in the first quadrant from (2, 0)…

A: We have to find the integral The parametric equation of given curve is

Q: Evaluate the line integral. { 4) ( y2 dx + x dy; C is the curve x =t2 - 1, y = 4t, 0 st s 1

A: The given line integral is ∫Cy2 dx + x dy; C is the curve x=t2-1, y=4t, 0≤t≤1

Q: ∫C  z2 / (z2 + 4) dz with C defined as z(t) = 2i + 2eit and 0 ≤ t ≤ 2π

A:

Q: Integrate h (x. y.2) = yzi+xj+xzk over the indicated path: the line segment from (0. 0. 0) to (1. 1,…

A:

Q: z = √xy, dz dt t², y = -t² then 2 2 2t²) =?

A: We have to choose the correct option from the given options according to the given information

Q: If f(x, y) = 3x? – by, then the total differential of f at x = 1 and y = -2 is : O df = 24 dx – 6 dy…

A:

Q: Find fr, fy, and fz. f (x, y, 2) = z In(x*y³ cos(52)) 4.3 fa = fy = fz =

A:

Q: 3. Evaluate the line integral sin(y) dx + (x cos(y) – sin(y)) dy, where C is the straight line from…

A:

Q: Use the Chain Rule to find dz/dt.z = sqt(8+x^2+y^2,    x = 4 ln t,    y = cos t dz/dt=

A: Please refer to the image below

Q: a) z=4x²-9x²y+2y³, com x=2 sen(t) e y=cos (t); b) w=xe, com x=4t², y=5e²¹ e z=2t². c) z=x y²+2x²,…

A: Introduction: When the independent variables of a function is again dependent on a single parameter,…

Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1) dy…

A: Using differentiation

Q: 2. Let f(x,y) 3x y. If C is the line segment from (1,1) to (2,3), evaluate r'dt.

A:

Q: Compute ∫C y dx + xy dy if C goes from (0, 0) to (1, 2) along the line parameterized as x = t, y =…

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

Q: 24. Evaluate . (x – y) dx + (x + y) dy counterclockwise around the triangle with vertices (0, 0),…

A: Given integral is, It can be represented using Green's Theorem as,

Q: 3. For x= In /t y=t2, find y'-y"when x=0.

A: To find: The value of y'-y" when x=0 . Given: The value of function are x=ln(t) and y=t2. Formula…

Q: Find fa, fy, and fz. f(x, y, z) = 3z ln (x³y³ cos(2z)) fx= fy= f₂ = =

A:

Q: -f(x,y, z) = 2z3 – 3(x² + y²)z + tan-1 xz , (1,1,1)

A:

Q: Q1: Use Green's theorem to evalute S. (xy + y2)dx + x²dy by the curve y y = x2.

A:

Q: Integrate h (x, y. 2) = yzi+xj+xzk over the indicated path: (a) the line segment from (0, 0. 0) to…

A: definite integrate calculus

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.