Let f(x)= x sin(1/x4)e−1/x2 and g(x)= e−1/x2 .Using the familiar properties of these functions, compute the limit as x approaches zero of f(x), g(x), f(x)/g(x), and f(x)/g(x). Explain why the results are surprising but not in conflict with the content of Theorem 5.3.6.1

Q: B) Test the functions continuity at the given poihts: (x²-x-6 1) f(x) 3D x * 3 ,at x 3, x 5 X-3 x =…

A: f(x)=x2-x-6x-3x≠35x=3

Q: Suppose that ƒ′(x)<= 1 for 1<= x<= 4. Show that ƒ(4) - ƒ(1)<=3.

A: Show that:

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A:

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A: given,        a.  f(x) = cot(x2)b.  x3+1

Q: Suppose f and g are positive functions. Is the following true or false? Vf,g:N → R f(x) E O(g(x)) =…

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A:

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A:

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A: horizontal compression means horizontal stretch.

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A: Answer

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A:

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A:

Q: 1. Examine the continuity of the fiunctions given below: (a) f(x)=x -5atx 2 (b) f(x) =2x +7atx 0

A:

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A: