Consider the graph of y =f(x).4+-8 -7 -6 -5 -4 -3 -2 -134 5=D3For infinite limits, use oo = ∞ and -oo =(а) limf(x) =(Б) limf(x) =x → – 3-(c) limf(x) =x → - 3+(d) x3 is a (type answer)to

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Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Show that the function f(x,y)=8x^2 y subject to 3x−y=9 does not have an absolute minimum or maximum. (Hint: Solve the constraint for y and substitute into f.) Solve the constraint for y. y = ? Substitute into f. f(x,y)= ? Determine the behavior of f as x approaches −∞. limx→−∞f(x,y)= ? Determine the behavior of f as x approaches ∞. limx→∞f(x,y)= ? Does this show that f does not have an absolute maximum or minimum? 1. No 2. Yes
Compute the lim(x,y)->(0,0) (4x2y)/(x2+y2)1/2
Consider g(x)=−7x3+7x2+9. a) limx→0−g(x)= b)limx→−1−g(x)= c)On what interval(s) is g(x) continuous?
7. Determine values of a, b, and c such that the graph of y = ax³ +bx² + c has a local extremum at (2, 11) and a point of inflection at (1, 5).
Evaluate the Limits: a) limt->-1(t2+3t+2)/(t2-t-2) b) limx->9 (9x-x2)/(3-x1/2) c) limx->-inf (ex-e-x)/(ex+e-x) Do Not Use L'Hopital's Rule
15.2.29 #13 Use the two-path test to prove that the following limit does not exist. lim(x,y)→(0,0)x+2yx−2y An x y z coordinate system has an unlabeled x-axis, an unlabeled y-axis, and an unlabeled vertical z-axis. A smooth surface labeled z = StartFraction x plus 2 y Over x minus 2 y EndFraction has an irregular shape. When x is negative, the surface is above the x y plane and in the positive y-direction of the x z plane, approaching both. When x is positive and y is negative, the surface is above the x y plane and in the negative y-direction of the x z plane, approaching both. When x is positive and y is positive, the surface is below the x y plane and in the positive y-direction of the x z plane, approaching both. x y z z=x+2yx−2y What value does f(x,y)=x+2yx−2y approach as (x,y) approaches (0,0) along the x-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
False. For example, the maximum off (x) = x 2 + 1 on [l, 2] is 5, occurring at x = 2, but f' (2) # 0. (c) True (d) False. For example, the function f (x) = 2x 2 - x 3 has a single local minimum on [-1, 3], at x = 0, but the absolute minimum on [ -1, 3] occurs at the endpoint x = 3.
In this example, we can combine the three simple results following the limit definition with the results in Theorem 1 to calculate the limits. We simply substitute the x- and y-values of the point being approached into the functional expression to find the limiting value.
Use limits to determine the equations for all horizontal asymptote. y = (1 - x2)/( x2 + 1)
5. Given the graph of g(x) = {√−x−2+1, x<-2 x2+2x+5, x≥-2 below, evaluate its limit as x approaches -2. a. 3 b. 1 c. the limit does not exist d. 5
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1. For what value (s) of x is the function f(x) = 4/2x2 - 6x not continous? 2. If the demand of firm is QD (p) = 50 -3p and its supply function is Qs (p) = 14 + 6p. What is the equilibrium? 3. Find Lim x2 -4x + 3/5

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Consider the graph of y = f(x). 4- -8 -7 -6 -5 -4 -3 -2 -1O 2 3 5 -2 For infinite limits, use 00 = 0 and -00 = (а) lim f(x) : (b) lim f(x) x → - 3 (c) lim f(x) = x → – 3+ (d) x = 3 is a (type answer) - to to