1-What are Univalent Functions .

Q: Give Three Functions  of Wronskian ?

A: To Give: Wronskian of three functions.   Wronskian:

Q: Determine the points at which the function is not analytic: (3z - 1) / (z^2 + z + 5)

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Q: Verify Rolle's theorem for the function f(x) = 2x2 – 20x + 33 on the interval [2, 8]. -

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Q: Differentiate the function.      f(x)  =        ______1______                            In x

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Q: Explain the Wronskian of 2 functions f and g ?

A: Let f and g are the two functions. The Wronskian of the n functions is the determinant of the matrix…

Q: III. Verify if the function is continous at the point. 1. f(x) = x³ – 3x² + 2x – 5 at x = 0 %3D %3D…

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Q: if f(x) is a function that is continous at (2,f(x)) then f(x) is differentiable at (2,F(2))   true…

A: Given statement is If f(x) is a function that is continous at (2,f(x)) then f(x) is differentiable…

Q: 2. What is the lilm f(x)?

A: From the given graph in extreme left side we can clearly see that. If x tends to minus infinity then…

Q: - Show that the function f(x) = secx.cscx odd or even

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Q: f(x, y) = /4 – x² – y² + V1 – x? -

A: To find the domain of the function, f(x,y)=4-x2-y2+1-x2

Q: Prove that f(x) = x 2 takes on the value 0.5 in the interval [0, 1].

A: We have to prove that f(x)=x2 takes on the value 0.5 in the interval [0, 1].

Q: 2. The owner of the rectangular lot wants to put a fence around the area using 120- meter barb wire.…

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Q: Determine the absolute maximum and minimum values of the function f(x) =+x the interval -2sxs2. x…

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Q: +1 Differentiate the function f (x) = In +1

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Q: Where is the function f(x) = if x 0 removable discontinuity? Is it a jump discontinuity?

A: A jump discontinuity occurs when right and left limit exists but are unequal .

Q: Find

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Q: 2 The function defined by f(x)= x-3x for all real numbers x has a relative maximum at x = %3D

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Q: Show that the function f : [0, 1] →[0, 1] given by f(x) = (x −1)2 has a fixed point. Can you apply…

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Q: B)Is w = Zez analytical function or not?

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Q: 3. Determine all the numbers c which satisfies MVT for the function f(x) = x3 + 2x2 – x n |-1, 2] on

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 3 Show that the function f(x) = Vx – 5 is one to one function. %3D

A: The objectives to show that the function f(x) is one to one function.

Q: 3) If a function is continuaus at x=a, then it is differentiaoe at x-a, yes? or NO? why ?

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Q: 4. Consider the functions g(x) = and . Determine (12)- (}),

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Q: Oz(-@) and Ør(@) are conjugate functions. That is, Px(-@) =Øx°(@) %3D and Oz"(-@) = , (@)

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Q: 4. Determine the function(s) whose domain are all real numbers. Choose all that apply. Linear…

A: Linear functions are of the form y=mx+c. There can be any value of x. So it's domain is set of real…

Q: and g:y → X. If gof -Ix => Show that f is one-to-one function %3D and 8 is surjective function ?

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Q: when that this 1x² + y² Shothathis sho (x, y) (0,0) and f(0,0) function is continous at (0,0)

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Q: Differentiate the function. h(x) = In(x + V - 12

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Q: Solve for a andb that makes the function continuous at every number in its domain f(x) = 2x+1 x5

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Q: Show that the function g(x) =x |x | has an inflection point at (0,0) but  g " (0)  does not exist.

A: Given function:                                 g(x)=x|x|   To find out the Inflection point=?…

Q: 3-The function f defined by 2. Is f is Continuous at x=| ?

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Q: 4. Show the function f(2)=21m(z) is differentiable or not differentiable at any points.

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Q: 28. Determine the absolute minimum value of f on the interval [-1/2,4]. f (x) = x³ – 3x? 16 7 -4

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Q: -, Determine the location and values of the absolute maximum and absolute minimum for the given…

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Q: Find a function for which f'(x) exists for all real numbers but f"(x) doesn't exist for all real…

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Q: Find a and b so that the function = { ax + b, 8x – 8x? + 4, ах + b, х -2 is both continuous and…

A: Continuity at x=-28-23-8-22+4=a-2+b-64-32+4=-2a+b-92=-2a+b→1

Q: In what degree of homogeneity is the function x + 4y

A: The given function is x+4y To find: degree of homogeneity of the given function.

Q: What is the value (i.e. what do we learn) from using the Wronskian on a set of functions?

A: Let F = { f1, f2, f3, ...fn} be the set of functions. 1. If W(f1, f2, f3,...fn) =0 Then we say…

Q: 5. Consider two entire functions with no zeroes and having a ratio equal to unity at infinity. Use…

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Q: prove two Function invezse each other fk)= (x-2)

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Q: Let [x² + 1 _ if x 1 f(x) - Is f differentiable at 1?:

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Q: (2) Find all the points of discontinuity of the function S(x) = } x + 2 (x2 – 4 1<x< 3 x2 3

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Q: If is an inner-product function , then : Select one: a. equals one b. equals zero c. is greater…

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Q: 9. Discuss the continuity of the function x 2 x2,

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Q: Verify Rolle's theorem for the function 2x2 – 18x + 29 on the interval f(x) = [2, 7].

A: Given,          The function is fx=2x2-18x+29 on the interval 2,7.

Q: 2- -2 d)

A: We have to find out all the graph

Q: х — 1 - 2. For f(X) calculate f-'(8) = ? %3D х — 3 -

A: Given : f(x) = (x - 1)/(x - 3), we want to find the function f-1 that takes the value y as an input…

Q: 3 Show that the function f(x) = Vx – 5 is one to one function.

A: The given function is: fx=x-53

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: