5. Let f(x)x² +1X 1when x > 0, and f(x)cos x when x < 0. Does fadmit an extension f on R, which is continuous at x = 0? Explain why.==6. Let ƒ,g be two continuous functions on R so that limx→0- ƒ(x) = 1,g(0) = 10, limx→1 9(x) = 2. Decide the value of limx→o gº f(x) if it exists.

5) Given that Noted that .Now we define so extension of is the following :So Thus we concluded…

Answered: 5. Let f(x) = ²+1 when x > 0, and f(x)…

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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Similar questions

Let f be a function that is continuous everywhere. The graph of the derivative of f is shown below. (0, 1.732) (-3, 0) (о, —1) TRUE OR FALSE. a) f is increasing on (-, -3). (b) f is differentiable on x = -3. (c) f" is decreasing on (-3,0). (d) f is concave up on (0, 0).
can you explain what this means step by step
4. Suppose f is differentiable at x = 10- (a) Show that f(xo+h)-f(xo) h f(ro+h)-f(xo - h) 2h (b) Show that lim h→0 lim h→0 f'(ro). = f'(ro).
The graph of the derivative of f' of a continuous function f is given in Figure 1. y = f'(x) 2- 2 /4 6. |-2 Figure 1 a) On what intervals is f increasing and on what intervals is f decreasing? b) At what value of x does f have a local maximum, and local minimum? c) On what intervals is f concave upward and concave downward? d) State the x-coordinates of the point(s) of inflection.
9. If f(x) is a continuous function on [a, b], differentiable function on (a, b), then there is at least a real number a
Suppose f is continuous everywhere, f’ is differentiable everywhere except at x = -1, and the graph of y = f’(x) is in the photo attached; Suppose f’’’ (1) is a nonzero real number. Is it positive or negative? Provide a brief justification for your answer.
6. Sketch a graph of a function f that satisfies the following conditions: of is continuous on (-00,00) o f(-2) = 1,f(0) = 0, f(2)= 1 f'(0) = 0 o o f'(x) 0 on (0,00) o f"(-2) = 0, f" (2) = 0 o f"(x) 0 on (-2,2) O lim f(x) = 2; lim f(x) = 2 8118 818 -10 -8 -6 -4 10 Jo -2 854 6 2 2 4 6 8 -2 -4 -8 -10 2 4 6 8 10
Sketch a graph of a function f that is continuous on (-o,00) and has the following properties. f'(x)>0 and f''(x) > 0 on (– ∞,2); f'(x) > 0 and f'"(x) <0 on (2,00) Choose the correct answer below. A. O B. OC. OD. AY -5

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