The composite function ƒ(g(x)) consists of an inner function gand an outer function ƒ. If an integrand includes ƒ(g(x)), whichfunction is often a likely choice for a new variable u?

Q: Find the largest Ś smallest values of the given function over the prescribed closed, bounded…

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Q: Compute the derivative of f (x) = x 3/2 using the limit definition.

A: fx=x32

Q: Find the critical numbers of the function. (Enter your answe g(x) = x² In(x) %3D X =

A: We find g'(x) using the product rule. g(x)=x2ln(x)g'(x)=2xln(x)+x21xg'(x)=2xln(x)+x

Q: What are the local minimum and maximum values of f. If an answer does not exist, use DNE.)

A: Consider f'(x) = 0.

Q: The definition of the first derivative of a function f(x) is: Select one: f(x+Ax)-f(x) a. f'(x) =…

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Q: . Let f(x) = x'6/3 – 19x337. Determine the largest n for which f € C" (n-times continuously…

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Q: Find the critical numbers of the function f(x)=x^5+5x^4-5x^3+8 and classify them using a graph.

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

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Q: A function fis defined by Sx. x<-2 g(x) = bx, x z -2 bx².

A: It is evident that we need to find the value of b if g(x) is continuous. Now,…

Q: f(x) = log,(\a² x ·7*) log, (ya²x •7*).

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Q: Let 'f be a continuously differentiable real valued function defined bx + a by f(x) ={ 5x x<1 x21…

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Q: differentiate the follouwing 243 a) f(x)=2x°-in/x|+3 arccos (X)

A: Since you have asked multiple questions in the same request, as per the policy, only the first…

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: Let A(x) f(t)dt, with f(x) shown in the graph below. -3- ** * T?

A: As per the fundamental theorem of calculus, given a function A(x)=∫0xf(t) dt, the derivative of this…

Q: The composite function f(g(x)) consists of an inner function g and an outer function f. If an…

A: The integrand function appears in the integration, hence integration helps to find the answer to the…

Q: Verify Mean value theorem for the function f(x)=4x3+x+2 over t interval [0,1].

A: Prove hypothesis of mean value theorem Differentiate continuous and value of c

Q: Find and classify all critical points of the function 3 f(x, y) = x³ + 2y - In(x³y³) Item 5.pdf

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Q: The interval over which the function f(x) = becomes continuous is %3D x+8 (-3, 0) (-3, 3) (-00,…

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Q: Show that if the graph of a twice-differentiable function ƒ(x) has an inflection point at x = a,…

A: Find the reason why the tangents lines fit well at the inflation points

Q: Prove that f(x) = other than the graphing method. x² – 1 is continuous at c = 0 by any method |

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Q: For what value of x does the funciton g(x)= (1/3)x^3-2x^2 strictly convex?

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Q: 1 Show that f (x) = is Libschitz function on %3D x +1

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Q: Let f (x, y) = 4-y² In(y–z²) %3D Draw a picture of the domain of this function.

A: x,y ∈R2

Q: Indicate all critical points of the function f(x)=∣∣x2−5∣∣.

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Q: Find a function flx) such that f(x) -llex and %3D 3. f(0)-- 주

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Q: In the Algebric terms what is meant by nvertible function?

A: Invertible function:

Q: Find a function f(x), such that f"(x) = 3sin(4x). %3D

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Q: find a point c satisfying the conclusion of the MVT for the given function and interval.

A: Given ,y = Cos x - Sin x      0,2πf(x) = Cos x - Sin x

Q: Show that if f(x) is a non-negative, increasing concavefunction, then ln [ f(x)] is also a concave…

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Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

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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: Let f: A→ B, where A= {1,-1}, B= {1,2,3}, and f(x)= 3×x²+2, find Range إجابتك * Codomain إجابك * Is…

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Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 16/x on the interval [0,…

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Q: If the function f(x) = {cos(2πx−a),x&lt;−1x3+1,x≥−1 is continuous, what is the value of a?

A: fx=cos2πx-a,  x&lt;-1        x3+1,    x≥-1 Since Cosine function is continuous for all real numbers,…

Q: Suppose that f(1) = -3, f(4) = -4, f'(1) = -3, f'(4) = -5, and f" is continuous. Find the value of…

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Q: Find the extrema of the function g(x) = x3 using any of the methods given in the above discussion.

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Q: Show that f (a) = is Libschitz function on r+ 2

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Q: Consider the relation x2z2 = arctan (xyz) + 4, which defines z as an implicit function of x and y,…

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Q: The function f(x, y) -{¹. - x² - y², 0, if if x² + y² 1 , is continuous

A: Given function is fx,y=1−x2−y2, if x2+y2≤10,             if x2+y2&gt;1. We have to check whether the…

Q: Find the Wronskian for the set of functions.{x, −sin x}

A: Given:  f(x1)=x and f(x2)=(-sinx ) The wronskian is given by the following determinant:

Q: Find the linearization L(x)of the function at a .

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Q: Show that the function f(x) = 1 – I - x² is continuous on the interval [-1, 1].

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

A: Given: The function g(x)= x |x| For x&lt;0, |x|=-x, thus g(x)=x(-x)=-x2 Also for x≥0, |x|=x, thus…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the g'(x) if: g(x) = 1 +t² dt 3x2

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Q: Compute the linearisation l(x) of f(x) = √1+x3 at x=2 and use this to estimate f(2.05)

A: Given function is: fx=1+x3 At x0=2 So the linear approximation is: Lx≈fx0+f'x0x-x0…

Q: Find the critical numbers of the function. f(x) = x8In(x) %3D X =

A: Consider the function  f(x)=x−8lnx

Q: Let f be a function of multiplicity 5 at P. Then at P, u(x) = has multiplicity: f(x) f(x)'

A: Let, then has form of, Now, differentiating the above equation we get,

Q: Compute f(c+h)−f(c) at the indicated point. f(x)=6x2​; c=4

A: Given : Function : f(x) = 6x2   To find : f(c+h)−f(c) at c = 4.