For each given combination of values lim x ->c f(x) and f(c), sketch the graph of a possible function that illustrates the combination. Answer 8 only! 5. lim f(x) = +oo, lim f(x) = 06. lim f(x) = +o, lim f(x) = 0%3D*+1-*+1+*+1-and f(-1) = 0and f(-1) = -17. There is a removable discontinuityat x = 1 and f(1) = 48. There is a jump discontinuityat x = 2 and f(2) = 3

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Answered: 6. lim f(x) = +o00, lim f(x) = 0 5. lim…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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9. Given that limx→3 f(x) = 2 and limx→3 g(x) = −5 compute the following limits:(a) limx→32f(x) = (b) limx→3f(x) − 4g(x) = (c) limx→3g(x) + 3−2 + 3f(x) =
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.
Let h(x) = (x2 - 2x - 3)/(x2 - 4x + 3). a. Make a table of the values of h at x = 2.9, 2.99, 2.999, and so on. Then estimate limx-->3 h(x). What estimate do you arrive at if you evaluate h at x = 3.1, 3.01, 3.001,......instead? b. Support your conclusions in part (a) by graphing h near c = 3 and using Zoom and Trace to estimate y-values on the graph as x--> 3.
Suppose g(x)<h(x)forx∈(0,1)∪(1,2) both limx→1g(x)andlimx→1h(x) exist. Must limx→1g(x)<limx→1h(x)? true or false
2. Give an example showing that, even if f0(c) = 0, it could happen that f(x) does not have a localmaximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?
5. Consider the function f(x) = |x| + 2 at x = 0. Provide a table of inputs and outputs that demonstrate the limitdefinition of the derivative, numerically
1. Broadly speaking, what are the Limit Laws, and why do they help us calculate limits?2. In Example 3, there is a step where the function x2 − 1x − 1is changed to x+ 1. But unlike the secondfunction, the first function is undefined at x = 1. How can we justify changing functions this way?3. Explain the flaw in the following calculation:limx→0x2sin(1/x) = (limx→0x2) · (limx→0sin(1/x)) = 0 · (limx→0sin(1/x)) = 0.
Find the constant c so that the limit limx->3 (x2+x+c)/(x2-5x+6) exists.
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
show that lim(x,y)→(0,0) (x^3+xy^3/x^4+y^2) does not exist.
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Find the limit for lim x -> 0 for cos(1/x)

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6. lim f(x) = +o00, lim f(x) = 0 5. lim f(x) = +oo, lim f(x) = 0 and f(-1) = 0 %3D and f(-1) = -1 7. There is a removable discontinuity at x = 1 and f(1) = 4 8. There is a jump discontinuity at x = 2 and f(2) = 3