In three to five sentences, discuss how the Limits of a Function is relevant to optimizing the area.

Q: 9. Let n(x) = -x² + 4x - 1 (a) Write n(x) in vertex form. (b) Sketch the graph of n(x).

A: As per our guidelines we are allowed to answer only three subparts of the given problem. Kindly…

Q: Find an equation of the tangent plane to the given surface at the specified point. z = 4x² + y² -…

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Q: Compute the second-order partial derivatives of f(x,y) =e4x2+6y2 82f 8x2 (x, y) 82f ?х у 82f дудх…

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Q: Separate the variables: Find the solutions of the following ordinary differential equations…

A: As per the guidelines,  I can only answer one question and rest of the questions will be reposted.

Q: Find the derivative of the function. 3 f(x)=√x - ³√x

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Q: 77. Explain why or why not Determine whether the following state- ments are true and give an…

A: Determine whether the following statements are true and give an explanation or counterexample.Since…

Q: Consider a function f(x) = −3x² + x − 1. (a) Using the definition of derivative (i.e. limit of…

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Q: Given f(x, y, z) = √√−7x + 3y – 3z, find fx(x, y, z) = fy(x, y, z) fz(x, y, z) = =

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Q: 4. Estimating limits graphically Use the graph off in the figure to evaluate the function or analyze…

A: We are authorized to answer three questions at a time. So we answer the first three sub parts.

Q: 2++ 32 N Graph of g The graph of the polynomial function g is shown. The function f is defined for…

A: In this question, we will find the local minima and maxima.

Q: Which of the following vectors is perpendicular to i? i+j i-j i - 2j -2i -2j None of the above

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Q: 3. Find teh vectors that satisfy the stated conditions. (a). Oppositly directed to 7 = (3,-4) and…

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Q: 26. Find a vector perpendicular to both a = [1, 2, 3] and 5 = [3, 2, -1].

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Q: find the derivative of the following by first expanding or simplifying the expression…

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Q: Factor 1296x4-14641 and solve the equation 1296x4-14641 = 0

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Q: Question 2.12) Is there some value of k for which the following function is continuous at x =-1? +k²…

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Q: Suppose that f(x) is a function with f(130) = 39 and f'(130) = 2. Estimate f(132).

A: f(x) is a function with f(130)=39 and f′(130)=2

Q: Find the derivative of the function. 1 f(x) = 3/5x² - 6

A: Given, derivtives formulas

Q: Find the derivative. Enter your answer without fractional or negative exponents. -3x6 + 12x4 - 10 x3…

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Q: 30,000 Р Suppose that the demand function for a product is given by D(p)=- a) Find the demand as a…

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Q: -|x|, h(x)=20-x², 4x-1, A) lim h(x) = x-5+ B) lim_h(x) = X115 C) h(3) = x≤-5 -5 3

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Q: y = cos (πx/2) and y = 1 - x²

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Q: Find the derivative of the following function. Make sure to state the differentiation rules that you…

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Q: Without a calculator, identify the given key features of the polynomial and sketch a possible graph.…

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Q: 1+2+3+ + n = n(n + 1) 2

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Q: 6. Refer to the graph of k below. -104 k(t) to- toliaupo oda y (a) Evaluate k(2). (b) Solve k(t) 27.…

A: The graph of the function is given.The aim is to find the a) Evaluate b) Solve c) Write the…

Q: (a) For what values of x is the function f(x) = x² - 25| differentiable? (Enter your answer using…

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Q: f(x) = x x + 1 P(-2, 2)

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Q: can you solve b ,c and d

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Q: Given that (a) (b) [{f(x) dx = 7 and ['f(x) [₁Fx f(x) dx [²F(x) dx - [₁1x) f(x) dx f(x) dx = 9,…

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Q: Find the normal vector to the tangent plane of z = 6eª²–2y at the point (4, 8, 6). ñ - (x, y, -1),…

A: given surface

Q: Determine the quadratic function of the form f(x)= a(x-h)² + k whose graph is given on the right.…

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Q: Determine whether the series converges, and if it does, find the sum: 47+2 5. Σn=0 5

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Q: Find the area of the region under the graph of f on [a, b]. f(x) = e-x/2; [-1, 6]

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Q: d 4. Determine sin√x dx Space on next page in radical form]

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Q: Let f be the function in the graph below. W Express in interval notation where f is differentiable.…

A: Given graph of f

Q: (1.1.39) Find the domain of the function F(p) = √2-√P.

A: given function is

Q: Consider the following two lines in space 1 2 = 6t , y =ut y = 4 +5₁ 2 = −1+S 72=X :17 2₂: X=15

A: Given that the following two lines in space

Q: 2.) Evaluate the function for the given value of the independent variable. Simplify your answer if…

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: If f(x) = , find f'(4), using the definition of derivative. f'(4) is the limit as x→ 4 expression…

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Q: Equations which can be written in the form can all be solved by integration. In each case it is…

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Q: domain f(x) = exp 1-e 1-el-x

A: f(x)=1−ex21−e1−x2

Q: The boundary of a lamina consists of the semicircles y = √√4x² and y = √√36 - x² together with the…

A: We have to find the x- and y- coordinates of center of mass.

Q: Given the differential equation y"+49y = −eºt, y(0) = 0, y'(0) = 0 Apply the Laplace Transform and…

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Q: give answers fore b,c,d

A: (b): (c): (d):

Q: find the derivative by using the product and or quotient rule  g(w)=e^w(w^3-1)

A: Given that function  to find the derivative of the given function

Q: Find the nominal interest rate for each of the following investments. Round the answers to two…

A: Given that :Table for Principal amount, compounding frequency and term is provided.To find : Nominal…

Q: An object dropped from rest from the top of a tall building on Planet X falls a distance d(t) = 13t…

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Q: Find u. v, uu, ||u||², (u · v)v, and u. (2v). u = 5i + j - 9k, v=i-4j + 5k (a) -44 (b) 107 (c) 107…

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Q: Find an equation of the plane consisting of all points that are equidistant from (2, -3, 4) and (-4,…

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