Ol a fundtion f is nt defined at X =a Then it is not continuQus at z= q

Q: efis continuous on the closed interval l-1,3]. If Fis an antiderivative of f. which c i F | of f…

A: In this question we will use basic of calculus i.e concept of definite integration. Solution of the…

Q: Let f(x+ y) = f(x)f(y) for all x, y e Rand suppose that f is di at x = 0.Show that fis everywhere di…

A:

Q: MY NOTES Find the x-values (if any) at which fis not continuous. Which of the discontinuities are…

A: Given: a) fx=lnx+1,x≥04-x2,x<0 b) fx=10-8e9-x,x>910-89x,x≤9

Q: let fERiema nn Tabland f(X)zo fok XE [aib] then Riemanninteral x 9.

A:

Q: A number c is called a fixed point of f if f(c) = c. Prove tha if f is differentiable on an interval…

A: We will solve the problem

Q: (i).Show that sin(x) is uniformly continuous on [0, infinity) by definition (ii). Show that ✓(x) is…

A:

Q: e theolem Let f be acontinyous fanchion o interior Tand citfble on ay - Point XEI then O f )<o…

A:

Q: (i) Using scaling and translation invariance only, find a, b,c such that for some Rie- mann…

A:

Q: Suppose f: [a,b] → IR is continuous on [a, b] and differentiable on (a,b) such that f'(x) 2 0 fur…

A: We have to use properties of integration here.

Q: The function f(z) =z is analytic O differentiable O it is not analytic O now where differentiableO

A: We have to check CR equation for the given problem

Q: 5b. Let a, b, c € R and a +0. Show that f : R → R, ƒ (x) = ax² + bx + c is continuous on R.

A: Recall: Definition of continuous function : Let m∈R be a constant. and Let f be a function defined…

Q: if a 4, 3. Determine the largest interval where j(x) = Vx² – 1 is continuous.

A:

Q: separa 1. Which of the following statements is CORRECT? A. Continuous functions are not…

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: The generalized product rule Use mathematical induction to prove that if y = uj uz U, is a finite…

A: If y=u1u2⋯un , then dydx=du1dxu2⋯un+u1du2dx⋯un+⋯+u1u2⋯un-1dundx

Q: (2) I Let (x, y) E R X R. Consider the following functions from R? to R? r((x, y)) = (-y, x) and…

A: We have to find the order of r and s. Here rx, y=-y, x and sx, y=x, -y where x, y∈ℝ. First, we have…

Q: %3D If f is continuous on [a, b), then ftf(x)dr =t[ f(x)dx Select one: O True O False

A: Solution:Given   If  f is continuos on [a,b]the ∫t f(x) dx=t ∫f(x) dxTo state :True or false.

Q: S (z – 3)2 – 2 z< 3 sin (z – 3) 3<I Let F (z) Then lim F (z) =

A:

Q: Putting V(x) = e¯*U(e*) show that 1 lim sup | V(x)| = lim sup |V(s)|ds. x00

A:

Q: and its der Foo the Fin d function f(z) = | - K i+ 2+eZ %3D

A:

Q: LARCALCET7M 4.R.008. ute extrema of the function on the closed interval. (Order your an ) = sin(2x),…

A:

Q: limf (z) =lim ylgn O ihs O السؤال 17 If f(2) is continuous at z then it must be differenttiable at z…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 5. Knowing that the functionf:R R, defined by f(r) = sin z has 0 as a fixed point the a contraction…

A:

Q: Q.No.1. (a) Let h(u, v) = In(n – u² + v) + v Vv – u , Where n=557find its domain and sketch the…

A: "Since you have asked multiple questions, we will solve the first question for  you. If you want any…

Q: 1-cosx , x*0 is continuous at x=0 Find k so that (x) =; 4x2 Ik, x=0 A 1/2 в) 1/8 (с) 3/4 D) 2/5

A: Use the definition of continuity to solve a given problem.

Q: 19 Jlgull If f is differentiable at a ,then f is continuous at a ylan O ihi O

A:

Q: (b) Is the function h(u,v) = cos(u)+ enu +sinh(u²) + yv+ enu , Where n is second digit of your arid…

A: A function is called continuous when there is no point of discontinuity in the entire graph of…

Q: 10. (True/False) For any continuous function f(x, y), we have fry = fyr.

A:

Q: Let z = 1+ iy. Determine whether f(2) is entire function or not? (Hint: Use Cauchy- Riemann…

A: Let  f(z) = u(x, y) + iv(x, y) Then the Cauchy-Riemann equations are ∂u∂x=∂v∂y and ∂u∂y=-∂v∂x

Q: Hfe Rfa, bj, prove the triangle ineguatity for integrats: , ) drs (Hint: Recall that ƒ - f - S…

A:

Q: Is the function h(u, v) = cos(u) + e™u + sinh(u²) + vv+ eu , Where n is second digit of your arid…

A: Use the properties that a term inside the square is supposed to no-negative number to get real…

Q: f (x,y) (x,y)# (0,0) F(x,y)= (x,y)= (0,0)

A: Use polar substitution and you will get that F is continuous at (0,0).

Q: All continuous f:[0, e function a>O impshding a2 S x*f(x*) dx = S xf(xIdx a) show +hat

A:

Q: 3 х2 у y? Which of the following is TRUE for the function f ( x, y ) = O a. It is continuous at ( 0,…

A: see 2nd step

Q: x*y° lim (x,y)→(0,0) f(x, y) does not exist, where f(x, y) = Show that (x2 + y4)3

A: To show that the below limit does not exist. lim x,  y→0,  0x4y4x2+y43

Q: 3x²y f(x, y) = {x + y² if (x, y) = (0, 0) if (x. y) = (0, 0) %3! norn (r u) uma f.

A:

Q: Assuming that z is a differentiable function of x and y, Let F(x,y.2) = In(x*y) – e" -ta tan Find…

A: Given,  F(x,y,z)=lnx2y-eyz-tan-1z Fx=∂∂xlnx2y-eyz-tan-1z     =∂∂xlnx2y-∂∂xeyz-∂∂xtan-1z

Q: À differentiable function f: (a, b) → R is uniformly differentiable on a, b if for every E>0 there…

A:

Q: -x^2, x < a Find the value of a such that f (x) = f(x) is continuous everywhere. %3D Vx, x2a

A: Given: fx=-x2,  x&lt;ax,   x≥a To Find: The value of a for which the given function is continuous…

Q: Ono. 6b) Proue Trut if f integrable [o,1, Hen on ei S znfcandx

A: Here f is integrable on [0,1] then we have to prove that limn→∞∫01xnfxdx=0

Q: Let F (z) =- tan (z-2) I<2 e +2 %3D 2 <z Then lim F(x) = %3D

A: Here, we have to find left hand limit(LHL) .

Q: 86 fos what valus of a,m, b does the functim f(x)= |フトフ0 mx tb てうxラ」 Satis fy the lagrange's mean…

A:

Q: x+y The function f(x,y) is not de_ned at the origin. Is it possible x²+y² define it at the origin…

A:

Q: where 9. Use the chain rule for multivariable functions to find f(u, v) = u + v, u(x, y, z) = x+y,…

A:

Q: Tet fiRt be defined by it R. * tyt i. Show that f is qutinyoys on IR.

A:

Q: The function f(z) =z is %3D it is not analytic O analytic O now where differentiableo differentiable…

A: We can check the differentiability and continuity of given complex function in the following way:-

Q: The function f(z) =z is analytic O differentiable O it is not analytic O now where differentiable

A:

Q: We know that Weierstrass's theorem is relative to continuous functions on compacts. This exercise…

A: Consider the given equation: Given P and Q are polynomials such that ∥P - Q∥R &lt;∞. The objective…

Q: x>0 If f(x) = { then f is: %3D :Select one a. continuous at x=0 b. not continuous at x-0

A: Here for the given function,    Right hand limit at x=0, is 1 And left hand limit at x=0 is 0.…

Q: 55. Let z = f(x – y. y - x). Show that az/ax + az/ay = 0. %3D 56. Let f be a differentiable function…

A:

Q: = Ek=0 for each n = 0,1,2,3 .…. Let X = {Sn]n = 0,1,2,3 ……} and Let Sn = EIn = 1,2,3 -.}U {0}. Let…

A: