Let g be an analytic function with g(-i) # 0, g(3) (-i) = -12, and g(4)(-i) = -36 . g(z) If f(z) then Res f (z)|z=-i = (z+i)4 3/2 None of these O 2 O -2

Q: What is the value of k so that the function f(x) is continuous at x=2 O-3 O - 3/2 1/2 0 1 T-2k f(x)…

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Q: Find f g and g of, where f (x) = x^2 + 1 and g(x) =3x + 2, are functions from R to R.

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Q: (@) Let FOR^ → R be a Function given by F(x₁, x,...,xn) = x²₁².. X²...x² x², where ) > x ²₁ =1. Show…

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Q: Let y=f(X) defines a twice-differentiable function and let y=T(x) be the line tangent to the graph…

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Q: Discuss the continuity of the function. f(x, y, z) = 1/(√x2 + y2 + z2)

A: Given rational function is

Q: Find the constant a such that the function is continuous on the entire real line. x 21 f(x) = lax –…

A: The function is continuous on the entire real line. We have to find the value of a.

Q: Let f(x)=x² -x² +x + 1 and g(x)= 3-х max{f(t):0sx; for 0 s x s 1} for 1 < x s 2 Discuss the…

A: Topic:- Functions

Q: Find the constant a such that the function is continuous on the entire real line. Ssin x g(x) = if x…

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Q: Determine the values of a and b such that the function (x -a ,x 1 Is continuous of all values of x.

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Q: The domain for the function ex y = x ln(3 - x) is {x/x 3} O

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Q: D. Discuss the continuity of the function g (x): 1 %3D on the interval [-1,2]. x2-4

A: Given, To discuss continuity of the function g(x)

Q: (a) Let f: R" → R be a function given by f(x₁, 2,...,xn) = x²₁₁x²2x², where n = 1. Show that the…

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Q: Let f(æ) = – 3x* In æ %3D f'(x) = f'(e²) =

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Q: Let the function f: R → R be defined by 1 x² f(x) = - 0, x = 0, x = 0.

A: Let us solve the given problem on continuity in the next steps.

Q: Find the constant a such that the function is continuous on the entire real line. (5x2, ах — 3, x 2…

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Q: We can find an analytic function f=u+vi such that 2u-3v+1 is not harmonic. False True

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Q: (a) Let f: R→ R be a function given by f(x1,x2,...,xn) = x².x²...x², where n = 1. Show that the…

A: Note: since you have posted multiple questions. As per our guidelines we are supposed to solve only…

Q: Let f(x) =x² t2X. Find all the values of ċ in the interval [2,0] such that f (c) =0.

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Q: 3. Determine the value of c such that the function is continuous on the entire real line. x+3, x 2

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Q: - (i) Determine whether the function f: R - R, f(x) = X+1 x*3 is surjective. x-3"

A: As you post multiple questions According to guidelines I only solve the first one.

Q: Let A > 0 be a fixed but unspecified constant, and let f(x) = xn= (In x)", x > 1. Compute f'(x).

A: our objective is to find the derivative

Q: Let f be a function defined on the real line R and suppose that it satisfies the condition If(x) –…

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Q: Consider a function f(x) = |x – 3|. a. Show that f (x) is not differentiable at 3. -

A: Given         f(x) =|x-3|

Q: 2. Find the constant a such that the function is continuous on the entire real number line x2- a2 w…

A: If it is continuous at x=a , then left and right limit must be same at x=a

Q: Let h be a function defined for all a 0 such that h(4) = -3 and the derivative of h is given %3D 22…

A: Given data: The given value is h(4)=-3. The derivative of h'(x)=(x2-2)/x. (a) Equate h'(x) to zero…

Q: 3. Let f (x) = x ² + 8x + 14. Find all the values interral C-G ,2) such that f (c) = 0 of ċ in the

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Q: Find the function f(x) such that f' (x) = x²e# with f(0) = 0. O (x² - 2x - 2)e* + 2 O (x2 + x + 2)e*…

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Q: Show that if n is a natural number and a, ß are real numbers with 8 > 0 then there exists a real…

A: Given that n is a natural number and α,β are real numbers with β&gt;0, then there exists a real…

Q: The value of c of f(x) = 2-, in the interval (1,3) such that f'(c) = %3D f(3)-f(1) %3D is 3-1 V340…

A: Given fx=2-3x given interval 1,3 f'c=f3-f13-1

Q: If the real part of an analytic function f(z) is x^2-y^2-y, then the imaginary part is О 2ху+x O 2xy…

A: We have to find the imaginary part.   According to our guidelines we can solve only one question so…

Q: Find and sketch the domain of the function f (x, y) = In(9 – x² – 9y²).

A: The given function,  f(x,y)=ln9-x2-9y2

Q: Sketch a graph of the function f(x) cos(z). -7/4 T/4 7/2 37/4 57/4 37/2 Z7/4 -1 -2-

A: We have to Sketch the given function

Q: 2 4. Find the most general analytic function f(z) of the variable z = x+iy whose imaginary part is…

A: 4. Given vx, y=y-yx2+y2 as the imaginary part of the complex function f(z).   To Find: The most…

Q: Let f be an analytic function on C: |z-1+i=2 with |f] 4 b. [f"(1 – i)| > 2 c. If"(1 – i)| < 2 d.…

A: here option (b) is true.

Q: Let f be an analytic function on C: z-1+i=2 with If] 4 b. |f"(1 – i)| > 2 c. If"(1 – i)| < 2 d. None…

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Q: (1) Let f(x) = 1,x > 0 with domf= R4+. Find the conjugate of function f(x). %3D

A: given fx=1x , x&gt;0 with domf=R++ claim- find the conjugate of function fx

Q: 1. Find and sketch the domain of the function. (f) f(x,y) = Vy – x In(y + x) (g) f(x, y) = 1-x² (h)…

A: See the attachment

Q: Let h(x) = cos x and g(x) = x - l. Compute the composite functions h o g and g o h, and find their…

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Q: Find c such that the function ² - 4 x c is continuous everywhere.

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Q: a) Show that f(z)=1/z is an analytic function.

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Q: If f is an analytic function and does not vanish in a domain D, then prove or disprove the…

A: To Prove/disprove: ∆|f(z)|=|f(z)|-1|f'(z)|2 for all z∈D, where f is a non-vanishing holomorphic…

Q: Let f(z) be a real valued function defined for satisfying f(1) = 1 and f'(2) = then lim f(z) =)…

A: Given function is, f'x=1x2+fx2 The above equation f'x is always positive which means fx  is always…

Q: Let f be a real-valued function continuous at the point a = (a1, a2) in R2. Keep a2 fixed and define…

A: We have given  real valued function continuous at a=(a1,a2) inR2 and define new function by…

Q: (iii) af A function is analytic if = 0. Prove that f(x, y) = az x-1-ty (x-1)²+y² is analytic.

A: The given function is f(x,y)=x-1-iy(x-1)2+y2. To Prove:  f is analytic, using the fact that "A…

Q: Discuss the continuity in R3 of the function f(x, y, z) %3D x2+ y2+z2 -1

A: Given: f(x,y,z)=1x2+y2+z2-1.

Q: g. The function f(x) = e- is continuous on the whole real line. %3D p(x) h. If f(x) is a rational…

A: g. Given,     The function fx=e-x is continuous on the whole real line.     True, the exponential…

Q: The function f(x) = -x* + 6x + 2 is concave %3D up on: Select one: O (-00, -V3) and (V3, 0) O (-1,…

A: The given function is f(x)=-x4+6x2+2

Q: 5. Find all analytic functions f such that Ref + Im f = xy.

A: To find all analytic functions f such that Re f + Im f=xy.

Q: 9. Show that if the analytic function f(z) has a zero of order N at zo, then f(z) satisfying g'(zo)…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.