What value of x makes the discontinuity of the function x2 – 4 f(x) = removable? x2 – x- 6 А) 3 В) -3 2 D None of the given choices E) -2

Q: b) Let f be a differentiable function of one variable, and let z = f(3x² – 5y²). Show that az əz…

A: Given  z = 3x2 - 5y2

Q: Use e – 6 definition and show that the function 4x² – y? if (r, y) # (1, –2) 2r + y f (r, y) = • 4,…

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Q: Which of the following is the function h(x,y) that satisfies the equation h(x, y).fxx+ X.fxy-fyy =0…

A: We will calculate all the partial derivativea and proceed

Q: 2. Show that the function u = e(xy) + VrY 4(y/x) provides the equation Pu = 0. dy? %3D -

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Q: at what points of R^2 is the following function continuous? f(x,y)=3x^2-xy^2+4y^3

A: We have to find the points at which f is continuous. Polynomial function is continuous every where

Q: Consider the function 8 · + 9. xy f(x, y) In which direction does the function f(x, y) increase most…

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Q: – x®y³, 6. Given f(x, y) = e®° - show that fxy = fyx.

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Q: Determine the linear approximation of f(x) = x' at x = 1. а. у3 9х +8 O b. Not in the list О с. у--…

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Q: Let f (2) be an analytic function, which is represented by f (2) = u (x, y) + iv (x, y) where z = x…

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Q: Use the linear approximation of f(x) = /2x - 3 about c = 2 to estimate the value of V1.32 Enter your…

A: Given that: f(x)=2x-3

Q: Determine the linear approximation of f(x) = x at x = 1. O a. Not in the list О b. у3 3х +2 с. у %3…

A: A detailed solution is given below.

Q: For what value of the constant c is the function f continuous on (-∞, 0)? cx? + 2x if x < 3 f(x) = {…

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Q: Suppose that f(x, y) = yvx* + 1 on the domain D = {(x, y) | 0 < y < x < 5}.

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Q: If f (x, y) = Vr³ + y³ In(x² + y²)e*in (zy+y') + x³y+ 10 , then f. (1,0) =

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: Suppose z is a function of x and y, and csc Vr² + yz = z"esin. Solve for dz and

A: A multivariable function is a rule that connects two or more variables. The partial derivative of a…

Q: (b) Suppose that f(x) = SBx? – 3 if if xS2 (Bx+ 2 %3D Find the value of ß so that f(x) is continuous…

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Q: Find the value of c which satisfies the conclusion of Rolle's Theorem with the given f (x) =x- 3x,…

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Q: Find the linear approximation of the function at the given point. ffx y)=-9x2-6y2+ 6 at (6,-10)…

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Q: -2? + 15z - 27 f(z) = 3z2 + 7z + 6 C, I= 3 What value of C would make f(x) continuous at z = 3?

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Q: Find D,y, given y = 3e" (2x – 5)*. D.y = 3e [4(2x– 5)'(2)]+(2r-5)'(3e") = 24e" (2x – 5)' + 3e"…

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Q: 4. Suppose that F(t) is a differentiable function of one variable. Define the function z(x, y) = e'F…

A: z(x,y) ey F (exy )diff wrt xdzdx = ey F' ex/ye.1/yzx = ey.ex/yyF' (ex/y)and diff wrt ydzdy= ey…

Q: 2. Show that the function u = p(xy) + Vry ý(y/x) provides the equation n, = 0. dy? U -

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Q: 2 3 tegral of the function xy d by x = 0, y = 0, z = C %3D %3D (2(5)

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Q: Show that the function y = x¹/², x > 0, is strictly concave

A: Given that y=x1/2 Differentiate both sides w.r.t x, y'=12x1/2-1y'=x-1/22 Again differentiate w.r.t.…

Q: If two functions Fand G are both antiderivative of the function h then they differ by a constant.…

A: Integration of h is F and also integration of h is G. So, F' = h  And, G' = h

Q: If f(3) = 15, f' is continuous, and I f'(t) dt = 24, what is the value of f(4)? %3D

A: In this question, f is a primitive function and we have to find f(4). So I am providing the…

Q: If we use trapezoidal rule for a function f(x) = x +2 1 - , then the approximate of J f(x)dx is…

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Q: of Let f(x,y) = xy° +7. Evaluate at (x,y) = (-7,1) and interpret the results. ду -

A: In this question we have find δfδy at (x, y)=(-7, 1)

Q: 5. Show that the function h(x, y) defined by 1 if a? + y? 1 is discontinuous.

A: We can solve this using R.H.L ≠ R.H.L

Q: A critical point xo, Yo of a function f is obtained when O Vf(x0, Yo) = 0 or Vf(x0, Yo) does not…

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Q: 1. Why is f not a function from R to R if a) f(x)= 1/x? b) f(x) = T? c) f(x) =±V(x² + 1)?

A: We'll answer the first question since the exact one was not specified. Please submit a new question…

Q: Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is?

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Q: 19 Suppose that Ts Cx) centered at 2 for f (x) is gicn by Ts Ca):345Ca-2)+5 Cx-2)?ょ2x-2)+(x-2) Than,…

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Q: 5 Show that the function h(r, y) defined by if r +y? < 1 h(x, y) 0; if r +y 2 1 is discontinuous.

A: For continuity of 2 variable function L.H.L=R.H.L=Function value at (x,y). limx→a+,y→b+…

Q: If Tn,0(x) = ao +a¡x+ a2x² +.. he function f(x) centered at x = %3D -) True p) False

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

Q: For what value of the constant c is the function f continuous on (-, 0)? S cx2 + 5x x3 – cx if x 4

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Q: Give an example of a linear function f(x)= mx + b, with m,b ±0 and an interval a<xsc where f(x)dx=0…

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Q: Suppose that f: R→R is a differentiable function, satisfying f(4)=3 and f(x) dx=6.

A: Given data: The first condition given is f(4)=3. The second condition given is ∫04f(x)dx=6. The…

Q: Зх +2y The function f(x,y)= is discontinuous at point x +y+1 (5,-3).

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Q: , Consider the function f(x, y) = x'y + y – 27y. f has v at (3/3, 0). f has ? at (0,0). f has ? v at…

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Q: If f (x, y) = Vr3 + y3 In (x² + y³)esin(zy+y') + x°y+ 10 , then f. (1,0) O 4

A: Properties of derivative  ddxex=ex ddxxn=nxn-1 ddxsinx=cosx ddx(lnx)=1x

Q: Show that the function d: RxR → R defined by d(x, y) = √x-y

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Q: Let a +b = 4, where a 0 for all x, prove that g(x) dr + g(x) dx increases as (b- a) increases.

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Q: 2. If f(x, y) is a function of y only, then S" S fdxdy Si fdy. %3D

A: Given query is to find statement is true or false.

Q: For which values of a e R is the function ++(). f(a + iy) = (a²z - ary) + i + ay an entire function?

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Q: If f(2) = 13, f' is continuous, and | f'(t) dt = 27, f(6)? what is the value of Answer:

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Q: 3 The antiderivative of the function f(x) = + 9x is x2 -3 4.5x2 + c 3 + 18.0a? + c 6- + 1.5x + c 3 +…

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Q: Find the value of constant c, if f(x) is continuous at x = 2 [cx? + 2x if x 2 -

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Q: Find values ofa and b that make B(x) both continuous and differentiable at x = 2: ax? B(x) ={ 6x + b…

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