WebDetermine whether f ' (0) exists. f (x) = {x sin 3/x if x doesn't equal 0. { 0 if x equal 0. WebWe can extend this idea to limits at infinity. For example, consider the function f(x) = 2 + 1 x. As can be seen graphically in Figure 4.40 and numerically in Table 4.2, as the values of x get larger, the values of f(x) approach 2. We say the limit as x approaches ∞ of f(x) is 2 and write lim x → ∞f(x) = 2. Similarly, for x < 0, as the ...

How do you differentiate f(x) = x^2sin(1/x), when f(x) is …

WebJun 3, 2024 · The function f ( x) = x sin ( 1 / x) is not 0 at x = 0 as it is not even defined there. But it does have a removable discontinuity there, i.e. lim x → 0 x sin ( 1 / x) = 0. … WebJun 21, 2024 · You can define f ( x) = x 2 sin ( 1 / x) and set f ( 0) = 0 to make f differentiable everywhere, but differentiating f using the formula f ( x) = x 2 sin ( 1 / x) doesn't tell you what is f ′ ( 0) because the formula is not applicable there. – Qiyu Wen. Jun 21, 2024 at 9:34. When you differentiate first, and then compute the limit, you are ... daniel teetor photography

real analysis - Question about $x \sin(1/x)$ at $x = 0$ - Mathematics

WebMay 16, 2024 · Firstly, Let us try and establish if the above limit exists. We can very easily show the limit exists and find its value: Method 1: Let z = 1 x then as x → 0 ⇒ z → ∞. So then, the limit can be written: lim x→0 xsin( 1 x) = lim z→∞ (1 z)sinz. = lim z→∞ sinz z. = 0. As sin(z) ≤ 1 and 1 z → 0 as z → ∞. WebDetermine whether f' (0) exists. f (x) = {x^2 sin 1/x if x notequalto 0, 0 if x = 0. WebTour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site birthday america