3. Given the following table about function f(x), approximate the value of f(1.25) by Lagrange interpolation. 1.4 1.7 y -2.5 | -0.7 1.2 | 4.8 1.1 1.3

Q: b) Specify the range of each of the following functions: (i) f(x,y) = e¯-z²-y² (ii) ƒ(x, y) = In(x²…

A: Note: " Since you have posted multiple question. As per our guidelines we are supposed to solve only…

Q: 1. Below is the graph of a function y = f(x). Estimate the area underneath the graph over [-3, 3]…

A: Since, you have posted multiple questions, but according to guidelines we will solve first question…

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A: Given, g(r,s,t)=3re2s/t g(1,1,1)= 3*1*e2*1/1 = 3e2 = 22.167

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A: Integrate marginal revenue and get total revenue

Q: - Is the function given by G(x) = Why or why not? continuous at x = 0?

A: We know that function is continuous only if its left hand and right hand limit equal, That is ,…

Q: h) f(x) = e4sin(5z+2)

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Q: The table gives the values of a function obtained from an experiment. X 6 7 8 9 10 11 12 f(x) -5.3…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 8. For what value of the constants A and B is the function f continuous on (-∞, ∞)? Ar + B for r 2

A: Please see the the answer below.

Q: What is the range of the function x) = X-3 O{xÎR|x'0} OIvIRly! 0} O tyÎRIy1 3} O{xIR|x'0}

A: Given function is                                         f(x)=1x-3 function is defined for all…

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Q: 54. Is the function given by SEx + 4, for x s 3, 2x – 1, for x > 3, g(x) continuous at x = 3? Why or…

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Q: 2. (i) Consider the following function of two choice variables Z-f(x,y) Write down the first order…

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Q: 2. Differentiate the following function: y = Jo tan 2x Hs dt. 1+t3

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Q: 2. The function y= fx) is continuous on its domain and some function values are given in a table…

A: Solution Given:-               x         1         2        4      6       y       0.1…

Q: Consider the function below. Approximate f(1.99) using a linear approximation. f(x) = 2x³ – 4x² – 3…

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Q: Given that flz) and g(z) are concave down functions. If we define h(r) = f(r) + g(c). Then h(c) is a…

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Q: The Range Rf for the functionf (x) = tanhx is:

A: Range of f(x)= tanh x

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A: Given: The function is fx=2x-3cosx. To show: f'x=1+3xsinxx Differentiate with respect to x:…

Q: The psd of X(t) is given by [1+ @? for | @|<1 Sxx (@) otherwise Find the autocorrelation function.

A:

Q: Given the following function: y = x^4 - 8x^3 + 22x^2 - 24x + 2 on [0, 4], find the absolute extrema…

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Q: 1. Use the function f (x) = x² – 3 to answer the following questions" A. Find the average rate of…

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Q: Suppose f is a linear function such that f(3) = 6 and f(7) = 1. Find the equation for f with respect…

A: Given,  f is a linear function such that f(3) = 6 and f(7) = 1

Q: For the function given in the below table, ,5 The approximation of f(x) dx using Mid – Point Rule is…

A: According to  Therefore, n=5∑i=12x2i+1-x2i-1fx2i-1+x2i+12=x3-x1fx1+x32+x5-x3fx3+x52 NOW

Q: Find the locations and values of all relative extrema for the functions with graphs as follows.

A: To find the relative extrema for the given functions in the graph.

Q: Consider the following. if x s 2 S2 - x |x² – 4x + 4 f(x) = if x > 2 Is f differentiable at 2? O Yes…

A: The given function is f(x)=2-xif x≤2x2-4x+4if x&gt;2 to find the given function f(x) is…

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Q: The marginal revenue (in thousands of dollars) from the sale of x gadgets is given by the following…

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A: Slope of tangent is obtained by differentiating the function f(x).

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Q: •10 16. The graph of f(x) is given below. Estimate f" f (x)dx using 5 subintervals with right…

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A: Given information: ∫08fx dx and the graph of a function,

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A:

Q: 2. What value of k would make the following piecewise function continuous? Explain your steps. S(x)…

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Q: 1 Is the function given by f(x) = ) 5x+1, for x s5, continuous at x= 5? Why or why not? %3D 5x- 19,…

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: Differentiate the following function with respect to x for y=2e^3x + 8e^9-2x .

A: Given equation is y=2e3x+8e9-2x Differentiate with respect to x.  then,

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A: Please refer the attached image for complete solution.

Q: (9) If f(x) is the slope of a trail at a distance of a miles from the start of the trail, what does…

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Q: a)Fit a curve of the form f(x) = Db-2.4 3.r to the following data -0.5 3.5 6.9 f(x)- -1 2.5 5 8.3…

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Q: Consider the following function. f(x) = x3/2 Find its average rate of change over the interval [1,…

A: The objective is to find average rate of change over the interval [1, 16].

Q: 1. Find the absolute extrema for the following function over the given interval: f(#) = * - + 2 +2…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 2. Consider the function below and the point (x, y, z) shaded in red. Is fa positive, negative, or…

A:

Q: Consider the following table of values for the function f (x) = Vx - 2. %3D Point f(x) A -2 -3.26 -1…

A: The table of the values for the function fx=x3-2 is To evaluate: The average rate of change over…

Q: 2.2 7. Using the table of values for the function g shown below to estimate f, g(x)dx using L3, R3…

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.