3. Consider the function f(x) = 23 if x = Q if x # Q. Prove that f'(0) = 0. Hint: Apply the conclusion in one of the problems in Problem Set 2. =

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A: Please follow the next step.

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A: Given :y''-2y'-3y=5cos2t

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A: The simple integration..

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A: We have to find out derivative

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A: limt→0sin t2t

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A: Quotient Rule : If  y = f(x)g(x)  then  y' = g(x)·f'(x)-f(x)·g'(x)g(x)2.

Q: Numerical Response #4: A close who will get to ride to grad in an girls in the limo then there are

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Q: 5 Does the series (²) n n=1 converge or diverge?

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Q: 3- show that the diff. equ. is homogeneous and Salve it (2x+34) dx +(y-x)dy = 0

A: To solve the given differential equation

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A: Given problem:- Jason acquired a $10,000.00, 91-day, Province of Alberta T-bill on its date of issue…

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A: Given ∫03xx2+2 dxSubstitute  u =x2+2→dudx=2x→dx=12x du:      =12∫1u du       =ln(u)2…

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A: Given

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A: As per guidelines we must answer only one of multiple questions given. Please resubmit the remaining…

Q: 15 //dx Sº

A: Topic:- application of integration

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A: Here we have to find the limit of a function.

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A: Since the student has posted multiple questions and does not mention any specific question, so we…

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Q: 2) If a + b + c = 0, show that a × b = b × c = cxā

A: Solve the following

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A: Here given that a limit problem and we solve this problem by using general property of limit.   Here…

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A: Solution

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A: I have stated the used formulas in the solution

Q: 121+ 18 + bh + S2 + b fl

A: We can solve this as follows:

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A: Given differential equation, dy/dx= x³/(2+y²) So, (2+y²)dy=x³dx

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A: Given, sin(∅)=2129 , π2&lt;∅&lt;3π2

Q: Ex.: Locate the centroid X of the shaded area shown. JİZZ 1 m

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Q: i) lim I-18 /976. T³ +1 Mar

A: Here is the solution:

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Q: What are the domain, range, and period of the function f(0) = 2csc(0 + 1)₂

A: solution:-f(θ)=2cscθ+π4=2sinθ+π4sinθ+π4≠0θ+π4≠nπθ≠nπ-π4Domain: all real θθ≠nπ-π4,…

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Q: If f* f(t) dt O 6 1 O -4 divergent = 20x √4x²+21 ∞ -4, then f(t)dt is X

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A: Use cos expand then find limit

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A: According to Bartleby guidelines I can only answer the first question of the given problems

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Q: Set up the intergal to find the arc length for f(x)=x^4+1 over [1,3]. Show all steps for setting up…

A: Arc Length , L = ∫x=ax=b 1+f'(x)2 dx .

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A: Let's find equation of tangent plane and parametric equations of normal line.

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Q: D-the result of the following 1² lim x-0 In (sec x) anther answer O 1

A: Here we have to evaluate the limx→0x2ln(secx)