F(X)=JX F: [o,2]-> show i fis lipschit z funcla or not find k to

Q: a) Demonstrate Gra phically the contimuity /Discontinuity of the tunction fx)- * ,0くxく」 1. 1+x)…

A: Authoring guidelines:…

Q: r cos(y) + y(e² - 1) x + 0 f (x, y) = ry x = 0.

A:

Q: Find the singularity of the function f(z)=(e^z-1)/z at z=0.

A:

Q: dr. Let f(z) =z. Find from z-0 to Z-4+2í alongthe curve C given Z=21 to z=2i

A:

Q: 30. Find the continuous function f(t) satisfying csin z for all r. 2+ f(t)dt = sin2015 /3

A: According to Leibnitz rule:

Q: Determine wheter f and are învers L41) f(x) = x-2, glx)=

A: solution:-Two functions f and g are inverse functions if and only ifg(f(x)) = x ,  for all x in the…

Q: Jerify Divergence Theorem for F = = (x + y') i – 2 xỷ + 2 yzk and the volu

A: Given: F⇀=(x+y2)i^-2xj^+2yzk^The plane, 2x+y+2z=6

Q: 21 (important) Find the fixed point for F(x) = ax + s. When is it attracting?

A: Given Fx=ax+s

Q: Evaluate both side of divergence theorem for cube define by -0.1< x. y.z<0.1 if D = 6xe2Y (āx + xay)

A:

Q: Find the linear approximation of the tunction fox) = NT-x at a-0 %3D and use it to approximate the…

A: We find f'(x) using the power rule.   then we find f(0) and f'(0)

Q: Po Prove that fcz) = zis coutinuous at z=z. O Prove that. fZキ2。 is dis continnity at z=Zo, where Zn

A: (1) we have to prove that                                                              f(z)=z2 is…

Q: Integrate f(z) over unit circle C and indicate whether Cauchy's theorem may be applied (4) f(z) =…

A: With the help of Cauchy theorem of integration we solve this problem.

Q: The function f (2) e? at z=0 %3D has pole removable singular point None essential singular point

A: The given function is  f(z) = ezz4

Q: find the divergence of F. F(x, y, z) = x²i + y²j+z²k div F = 2(x + y+ z) div F = 3yz? + 2y sin z +…

A: Topic = Derivative

Q: 2. Let F = 3.xyz i – 4xyz j + 2xyz k . Find div F and curl F. -

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Q: over the open surface S given by the upper part (only) of the intersection of ti of the function z =…

A: Introduction: Stokes Theorem (also known as Generalized Stokes Theorem) is a statement about the…

Q: Let f(x) = -cos(x). Compute ộ = coto + C1T1 where to = 1 and 1i = x. %3D Compute the discrete…

A:

Q: Let F(x, y, z) = (sin(xy), cos(xy), sin(xyz)). What is the divergence of F at the point (T, 2, 0)?…

A: Given : F→x,y,z = sinxy, cosxy, sinxyz

Q: Find the orthogonal trajectories of the families of r e, where a being a parameter. (0)

A: Orthogonal trajectories are another family of of curve which are perpendicular to the the original…

Q: Find the Wronskian of the functions f(t) = et sin(t) and g(t) = et cos(t). NOTE: Your answer must be…

A:

Q: Let H(x) integral ,for -2 ≤ x ≤2.Use geometry to evaluate H(2).

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: DNE.) +2+ f defined on |-1,3] maximum (x, y) = minimum (x, y) = Need Helo?

A:

Q: tion z2 – (x2 + y2)2 and let p = (0, 0, 0). ermine the set Tp(Zf ) of all tangent prs to Zf at p. Is…

A: Sol

Q: Show that f(x,y)=exyx is differentiable at point (1,0) using the definition of differentiability.

A: A function is called differentiable, if the derivative of function exists at each and every point in…

Q: Find the guneral antiderivative of the funchion. (check your answar answer by differentiation.) 14)…

A:

Q: Test the function def ined by f (x,y) = - x- 4y for its homogeneity. If it is homogeneous, give its…

A: Find your answer below

Q: Show that the Dirichlet function f defined on [0 , 1] by f(x) = { 1 if x is rational 0 if x is…

A:

Q: 4. ·| cotl t• dt 0. lim limitinin değeri kaçtır? n In(x + 1) a) 3 b) 1 c) O 2 d) 4 Boş bırak

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Q: 1 Find the local linear approximation of f(x) = , at 3+ 1 Tg = 2, where Az = I- 2. NOTE: Enter the…

A:

Q: 2. Let f(2) = 2°e* z + 0. What type of singularity does f(z) have at z 0? (Justify.) What is the…

A: the point z=0  essential singularity.

Q: (2) Use Green's theorem to calculate f. F - di for F(x, y) = (x2 + y, e") and C the boundary of the…

A:

Q: 3. Compute x In x da both analytically and numerically. Use trapezoidal, Simpson's 1/3, Simpson's…

A:

Q: Dete‎rmine if f (x, y) = ={(xsi‎n3y)/(x‎2+y6), (x, ‎y) ≠ (0, ‎0) ={1, (x, y) = (0, 0) is‎…

A: Solution: A graph for a function that's smooth without any holes, jumps, or asymptotes is called…

Q: Show that the function f(x + iy) = Vlæ|ly| satisfies the Cauchy-Riemann equations at the origin but…

A:

Q: Q2 A) for F= 2xi-3Y3+K %3D prove That div( curl È)=0

A: Given :          F→ = 2x i - 3y j + k   To prove that div(curl F→ ) = 0

Q: (b) Let F = (-yx² , xy²). Let D be the annulus 1< x? + y² < 4, and let C be its boundary. Evaluate…

A: Greens theorem

Q: B. Use Green's theorem to evaluate f (x²y)dx + y²dy Where C is close path formed y = x and y = x³…

A: Above first question is solved. Solving more than one question is against the policy of bartleby.

Q: Find the divergence of F(x, y, z) =(a -1 Y, y? + 1' 3xz2 + 2y ) at (2,0, – x COS

A:

Q: Osx 5. Use the Second Fundamental Theorem to find : S V4- t3 dt (7 pts)

A: follow next step

Q: Supose z is implicitly defined by the eq qy+ 3x*+ XyZ + 3Z=9 in an emvoment of the point P(0,3) in…

A: In this question we will use basic of vector calculus i.e concept of directional derivative. We will…

Q: Suppose that z = f(x, y) is differentiable at the point (27, 81) withf,(27, 81) = 2 and f, (27, 81)…

A: Given that:                            z=f(x, y)fx(27, 81)=2fy(27, 81)=-6x=t3y=t4

Q: Defn `x→- `xj diverges to minus infinity" VR>O 3N, such that Vj zN *j<-R 8;<- R Hw7 het x; = - 8j…

A:

Q: Estimate x using the trapezoid rule withn=4 a. Type equation here. Redo 9 using Simpson's rule. a.…

A: Given  f(x) = x3  a = 0 , b = 4 , n = 4

Q: %3D a) Find fyxyx for f(x,y) = In(xy) – cos (xy) at (1,t).

A:

Q: -if f₁ (t) properties of Fourier transfor eat alt) JF.T = $ fit) ējut dt = - feat. ejust dt е ماز-…

A: Topic:- calculus

Q: Find the work done by F over the curve C in the direction of increasing t,where F=-5 yi+5xj+8z°k and…

A:

Q: Assume x and y are functions of t. Evaluate dt for 4xeY12-In 729+61n x, with the conditions -6, x-3,…

A: Given that 4xey=12-ln729+6 lnx and the conditions are dxdt=6 , x=3, y=0  find dydt

Q: Q5:[10M] A) Let f: [0,2] → R be defined by f(x) = {1 if XEQ 20 if x # Q Show that f is not Riemann…

A:

Q: Consider a Lorenz curve given by f(x)=x^n for 0≤x≤1 and n≥1. What happens to the Gini index G.I as…

A: Consider the given function. fx=xn The Gini index is defined as, GI=2∫abx-fxdx