Show directly that the given functions are linearly dependent on the real line. That​ is, find a nontrivial linear combination of the following functions that vanishes identically. f(x)=29, g(x)=3sin^2, h(x)=4cos^2x   enter the non-trivial linear combination (12)(29)+ (     ) (3sin^2x) + (    ) (4cos^2x)=0

Q: Give Three Functions  of Wronskian ?

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

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A: To solve an equation  f(x)=0 using derivative of function, we can use the formula…

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

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A: Given that , the functionfx=2x2,x≥1ax-7,x<1We have to find constant a such that the function is…

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A:

Q: Q1 Prove that the derivative of (2x +1) 2 is 4 (2x + 1) by using first principle derivative.

A:

Q: - Prove that the derivative of (2x +1)2 is 4 (2x + 1) by using first principle derivative.

A:

Q: Find all critical points of the function f(x) = x4 – x-

A: Critical point is 5/4 Explanation is given below

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A: We have to find the derivative

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A: Given that, f'(x)=4x3-9x

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A:

Q: Suppose (2, -1) is a critical point of a function f with the continuous second derivatives. If fxx…

A: We need to choose correct option.

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A: Given,     f(x)=2x13+4x1x22-10x1x2+x22

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A:

Q: Find the derivative. using chain rule 7 5. у %3 V1-14x2

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A: The given function is; f(x)=x2/4 +8 - 5x5/3 +5x3.

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A:

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A:

Q: State why the function 2z2 - 3z + e-z is analytic everywhere.

A: See the answer below

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A:

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A:

Q: Q1 Prove that the derivative of (2x +1)2 is 4 (2x + 1) by using first principle derivative.

A: as per our guidelines we are supposed to answer only the first question. Kindly repost other…

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Q: Find the partial derivative. revIlzy

A: We can find the partial derivative as below.

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A:

Q: 1. у %3D 4x2 — 3х — 2.

A:

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A: Given : The functions and the points.

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A:

Q: Find any critical numbers and apply the First Derivative Test to identify any relative extrema. а)…

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

A: To create a linear function

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Q: determine maximums and minimums by the Second Derivative Test, we differentiate y"=72 / (2-8)3…

A: topic  - local maxima and minima

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A:

Q: Find the critical points of the function f(x)=x2lnx.

A: We need to find the critical points of the given function.

Q: Find the derivative. (Hint: do chain rule. ) * 12° dt 6x 8x6 12x/2

A:

Q: 4. Find the maxima/minima of f(x) = x³ – x using both 1st and 2nd derivative test.

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A: Given  f(x) = ax3-bx2

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A: To solve the following derivatives using chain rule and product as well as quotient rule.

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A:

Q: Find the critical points of f(x)=3x^4 -4x^3 +5 and use the first derivative test to determine local…

A: Given,          fx=3x4-4x3+5