1. Simplify the following without using a calculator. A. In(e-³) B. In(e². e³) C. eln(2) D. eln(5)+ln(3) E. e³ ln(2) F. e-In (2)

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A: This is an optimization problem, we use first derivative to find critical values and second…

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A: Please see the below picture for detailed solution.

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A: Domain:- The set of all those input variable such that the function at those values exists.Range:-…

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A: Equation of tangent line to fx=-2x3-3x2-2x, at -1, 1

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A: Demand function p=1692-13x2Average cost c=900+14x+x2

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A: Consider the following function.gx=3x3-8xTo find the first and second derivatives of the function.To…

Q: 3. The limits below do not exist. Verify this by showing two different pathways that result in…

A: limx, y→0, 0xy2x2+y4along path x=0=lim0, y→0, 00· y202+y4=lim0, y→0, 00=0along path x=y2=limy2,…

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A: Use the Bisection Method to approximate, accurate to two decimal places, the value of the root of…

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A: If gx=cosx, then to find g'x and g'4.

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Q: 2. Find lim (√t+3, In(2 — t), ²). t-x

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Q: m Homework Assign... mework Find the first partial derivatives of f(x,y) = 5 e x³y 11 Mail - kaleb…

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Q: only

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A: We can find the particular solution in the below steps using the appropriate method.

Q: Use the e- definition of a limit to compute the value of the following limits: 1. 2. lim 2² – 5

A: We  will find the required  limit.

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A: Let's solve given diffential equation by using Laplace transform.

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A: Here we have to use the bisection formula for solving the question.

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Q: 2. Find (F(r(t))) when F and r are the functions given below. (a) F(x, y) = sin(x) + cos(y) and r(t)…

A: According to our guidelines,i can solve only first please reroute the remaining question.

Q: 5. Let U(x, y) be the utility function for two goods, X and Y, given by xy² x- Y U au au Find the…

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A: Topic = Differential Equation

Q: lim (1+1)* 148

A: Please see the below picture for detailed solution.

Q: For f(x) = 3x² + 8x + 7, find the equation of the tangent line at the following values of x. (a) x =…

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