Find a bijective function f : R^+ → R^+ different from the identity function and has the property f = f^−1

Q: |Consider the function f(x) = x|x|. a.) On the interval (-∞,0), f"(x) = b.) On the interval (0, o),…

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Q: Give Three Functions  of Wronskian ?

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

Q: The set of functions {sin nx}, n = 1, 2, 3, ... , is %3D orthogonal on the interval [ -n, n]. Show…

A: Given- The set of functions sin nx, n = 1, 2, 3, ⋯, is orthogonal on the interval -π, π To Show-…

Q: Find the 3rd derivative of the function y = (3x³ – 7x2 +5) (x²+5) O y" = 120z2 - 168z + 90 %3D O g"…

A: Recall:Firstly product the givern term and find function of 'x'   i.e;   y=fxSome formula:∙ddx…

Q: Find the second derivative of the funcion. y%3D

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Q: Show that f1x2 Vin x is right-continuous at x = 1.

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Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

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Q: In x y = 1+ In x

A: I have written the formula used , here f'(x) and g'(x) are derivative of f(x) and g(x)…

Q: The function f, where f(x) = secx, has domain 0<x< and has inver %3D f-l, where f-(x) = sec-lx. Show…

A: The given function is f(x)=sec x and the inverse function is f-1(x)=sec-1x. To prove that…

Q: Explain why the function f(x)=cos.x-xmust have at least one zero on the interval [0,5]

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Q: 1. Determine where f(x) = arcsin (x² – 2x) is increasing. %3D

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Q: Define a weakly quasi-concave on a Cobb-Douglas Function

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Q: Show that the functions are continuous on their natural domains with examples?

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Q: Differentiate the function. 3. %3D In(x)

A: Given y=3ln(x)differeniatey'=ddx3lnxy'=3ddx1lnxApply exponent rule:  1a=a-1y'=3ddxln-1xApply chain…

Q: 7. Differentiate the function using quotient rule. хех y = x + ex

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Q: Differentiate the function using product rule. f(x) = (2x³ + 5x) cos x %3D

A: Given : fx=2x3+5xcosx

Q: Find the derivative of f(x) = (1 + 7x2)(x − x2) in two ways. 1. Product Rule 2.Perform the…

A: For product rule we use u=1+7x^2 and v=x-x^2Product rule = u'v+uv'Answer: f'(x)=1-2x+21x^2-28x^3

Q: f(x) = (2x3 + 5x) cos x

A: Given function is fx=2x3+5xcosx. Differentiate using product rule ddxf·g=f·ddxg+g·ddxf

Q: What are the removable singularities of the functions ?

A: Topic:- function

Q: Define wronskian of Two Functions?

A: Wronskian of two function: Let f(x) and g(x) be two differentiable functions, then wronskian of f(x)…

Q: By using quotient rule, differentiate f(x) = (2x* – 7x² + 3x)(x² + 1)-1. Hence, find the gradient of…

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Q: Show that given functions are orthogonal on the indicated interval. f1(x) = ex,   f2(x)= xe-x - e-x…

A: given functions are orthogonal on the i interval [0,2] are f1(x) = ex,   f2(x)= xe-x - e-x .

Q: Give an example of a function that is not Riemann integrable.

A: To give example of a function that is not Riemann integrable :-

Q: Find four relations from {a,b} to {x,y} that are not functions from (a,b} to x, y}

A: We have to find four relations from {a, b} to {x, y} that are not functions from {a, b} to {x, y}.…

Q: Define Wronskian of Linearly Dependent Functions?

A: We have to define the Wronskian of linearly dependent functions: Let f1 ,f2 ,...,fn be n real or…

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

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Q: what is the quadratic polynomial for the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1) (show…

A: We will find out the required value.

Q: Use the linear approximation to estimate Af = f(3.2) – f(3) for f(x) = 1+x² * (Use decimal notation.…

A: Given: f(x)=81+x2

Q: Find four relations from {a, b} to {x, y} that are not functions from {a, b} to {x, y}.

A: It is given that the two sets are {a, b} and {x, y}. It is known that if A and B are the sets then…

Q: Differentiate the function f (x) = 4 cos 3x - 3 sin 4x. %3D O -4sin 3x -3cos 4x O -12(sin 3x + cos…

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Q: Show two ways to differentiate ƒ(x) =

A: The function f(x)=1x10. We have to differentiate this function.

Q: Derive error formula for functional relation?

A: We have to derive derive error formula for functional relation

Q: Determine the values of a and b such that the function is differentiable on (-, x2 +b, x〉2

A: Given piecewise function is:A function is differentiable when it is continuous and the left and…

Q: Use derivative to show that fx)= In(x²1) %3D is one-to-one.

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Q: Differentiate the following functions using product rule. 1. f (æ) = (3x – 9) (x – 6) 2. ƒ (x) = (æ³…

A: The product rule of differentiation is given by: ddxf.g=dfdx.g+f.dgdx

Q: Differentiate the function y = (x + 8) In (x +8). y' = %3D

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Q: Find the averuge valuc of the function fcx)-4x4 on the interval [2,6],

A: Given : fx = 4x4

Q: Create a linear function over [2,4] that has an area of zero.

A: To create a linear function

Q: Find the exact location of all the relative and absolute extrema of the function. f(x) = 2x – 2…

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Q: Find the domain of the function. 4) f(x) = x2 + 3 A) (-«, -3) u (-3, ∞) C) (-3, «) 4) B) (-*, «) D)…

A: We will find out the required domain.

Q: Show that: sec²x + csc²x = sec2x.csc2x %3D

A: To show: sec2x + cosec2x = sec2x·cosec2x

Q: prove: f(x)=5x is continuous at x=2     note: please prove this in theorem format(two columns)

A: Consider the given function. y=5x Now, check the left first.…

Q: example of a function fi[g1] IR Give which is not integrable

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Q: estimate the type of the function at the interval {(1,2), (2,5), (3,5), (4,7)} is it: 1-1 or onto..?

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Q: Vx + y + 1 f(x, y) ,æ In (y² – x) х — 1 -

A: Given: fx,y=x+y+1x-1,xlny2-x A function f(x,y)=Mx,y,Nx,y is said to be continuous on the points…

Q: 2 Vtan 0 de

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Q: Find 1" and 2nd order partial derivative for the function ax²+by²+2hxy and also verify дхду дудх

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Q: Give an example of a function that is integrable on the interval [−1, 1] but not continuous on [−1,…

A: Let fx=x       Greatest integer function. Now, ∫-11x dx=∫-10x dx+∫01x dx=∫-10-1 dx+∫010…

Q: Find four relations from {a,b} to {x,y} that are not functions from {a,b} to {x,y}.

A: Given: Let A=a, b and B=x, y To Find: Four relations from A to B that are not functions.

Q: Determine if continuous f (x) = V4-x at x=0 %3D

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