Prove that lim 12 √16x +9y¹2 2 6 4x² +3y does not exist by showing that the limits along different (x,y) → (0,0) curves are distinct or not equal.

Q: The class outing ticket includes a snack-pack with three items, a cooldrink, chocolate and then…

A: Given tree diagram shows all the possible combination of "cooldrinks", "chocolates" and "chips or…

Q: For each positive integer n, define an = n² sin +∞ 1. Determine if the sequence {an} converges or…

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Q: D O O Question 8 Evaluate the limit limo 04 0 2 00 0/1/201 3 tan (+h)-tan (3) h by recognizing it as…

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Q: If z² - 3yz² + xyz -2=0, find Az дz and дх ду

A: The objective is to find the Partial derivatives.

Q: An applicant receives a job offer from two different companies. Offer A is a starting salary of…

A: Given problem:- An applicant receives a job offer from two different companies. Offer A is a…

Q: The graph shows the depth of water W in a reservoir over a one-year period as a function of the…

A: Concept: The average rate of change : The average rate of change function explains how quickly…

Q: Use the graph of y = f(x) for problems 7 and 8. 1010 lim f(x) = 1; HI-4+ lim f(x) = 1; 41144 Use the…

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Q: Consider the function f(x) = (4 - 5x)7. Find the second derivative f"

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Q: 7. A jar contains black and white marbles. Two marbles are chosen without replacement. The…

A: Solution is given below

Q: Find the volume of the solid obtained by rotating the region enclosed by the curves y = 1 and y =…

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Q: Determine the interval of convergence of n=1 (x - 5)" n²

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Q: 4. Verify if the following equations general solution: are exact and find the 2 9. 2xydx + (1 + x²)…

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Q: 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A: Topic = Derivative

Q: 3. Find the domain of f(x) = 1- 1 X X

A: We have to find the domain of f(x)

Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

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Q: This exercise uses the radioactive decay model.. The half-life of radium-226 is 1600 years. Suppose…

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Q: bounded by x² + 2y = 4 and - Sketch the area x+y+2=0 and determine: d) area using using horizontal…

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Q: Evaluate the double integral. Int[2,6] Int[-2,2] (-u+5v) dudv

A: I have stated the used formulas in the solution

Q: Which of the following graphs represents x = -3?

A: Question: Which of the following graph represent x= -3 ?

Q: Find the transfer function, G(s)=C(s)/R(s), corresponding to the differential equation, d³c d3 +3.…

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Q: An object moves with velocity as given in the graph below (in ft/se How far did the object travel…

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Q: Find the derivative of the function: f(x) = ln X x+1* Is there a shortest way? Please explain.

A: We can find the answer in the following steps.

Q: Question 14 Each side of a square is increasing at a rate 3 in/s. At what rate is the area of the…

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Q: This exercise uses the population growth model. A certain culture of the bacterium Streptococcus A…

A: Question: (a) Find an exponential model for the number of bacteria in the culture after t hours. (b)…

Q: 5. S (2x²+1) x3-3x+2 dx

A: Here we have to find the integral.

Q: [2 2x log 2x dx

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Q: Which of the following polynomials has an odd degree and a positive leading coefficient? W O -10-947…

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Q: Find the y-intercept of a quadratic function containing the following points: (2,5), (1,0), and (-2,…

A: Topic:- function

Q: Define the force field F(x, y, z) = . a. Find the divergence and curl of F. b. Let C be the directed…

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Q: A particle is moving with acceleration a(t) = 30t + 10. its position at time t = 0 is s(0) = 7 and…

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Q: 9. dt + 을 = COS t + Answer: s = sin t + 을..

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Q: Find y′′ y = -3x4(4x+6)2

A: Recall: Power rule; dxndx=nxn-1 Given, y = -3x4(4x+6)2

Q: On Integration of Rational Fractions. Distinct linear factors Repeated linear factors x+8 7) 2+ 1²²…

A: 6) Given:       x+8x2+x-2=x+8x-1x+2 The partial fraction decomposition is:…

Q: A producer of pedal-powered ice cream makers has determined that the revenue from the production and…

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Q: An eliptical-shaped path sumounds a garden, modeled by X-20²0-RP where all measurements are in feat.…

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Q: Differentiate y = √x + √z 01 O 2√x+1 A+ 2√x + 2√x O 2√x + √x

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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Q: What are the coordinates of the x-intercept of the equation 2x - 3y = 8? (-4,0) (-8/3,0) (0,-8/3)…

A: Please see the below picture for detailed solution.

Q: Set up the triple integral in spherical coordinates that solves the volume of the solid bounded…

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Q: 2 8 X2 x4 + x2 dx

A: To solve the given integral.

Q: IV. Fill in the blank to make each statement true. Use correct notations. 3. If a polynomial…

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Q: The legs of a right triangle have lengths 3 cm and 4 cm, respectively. A rectangle is inscribed in…

A: This question can be solved using the concept of maxima and minima.

Q: below

A: We have to choose the correct option from the given options according to the given graph of line

Q: Find the equation of the parabola described below. Find Kthe two points that define the latus…

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Q: IV. Fill in the blank to make each statement true. Use correct notations. 2. If ƒ(x) = 1 – log5 x,…

A: The objective is to find inverse of f.

Q: A student was asked to determine the y-intercept for the logarithmic function f(x) = log₂(x + 3) +…

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Q: Onsider the function f(x) = -4x²+7x+6. Interpret the e average rate of change from x = -7 to x = 7…

A: Topic:- application of calculus        Definition :-  The tangent represents the instantaneous rate…

Q: X

A: Slope intercept form of line  y=mx+b Here m=slope, b= y intercept

Q: 3. Find the domain of f(x) = = 1 - 1- x X

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Q: B If f(x) has a local minimum at ra, then which of the following must be true? O f'(a) > 0, f"(a) 0…

A: We have to find the correct option.