WebApr 24, 2016 · How do you differentiate f (x) = x2 sin( 1 x), when f (x) is defined as 0 for x = 0? Calculus 1 Answer Jim H Apr 24, 2016 You'll need to use the definition. Explanation: f '(0) = lim h→0 f (0 +h) − f (0) h = lim h→0 f (h) − f (0) h In this case we get f '(x) = lim h→0 (h2sin( 1 h)) −0 h = lim h→0 hsin( 1 h) The limit hence, the derivative is 0. WebMar 21, 2016 · Explanation: To show that f (x) = x is continuous at 0, show that lim x→0 x = 0 = 0. Use ε −δ if required, or use the piecewise definition of absolute value. and lim …
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WebYes, the cubic function is differentiable. For example, the function f(x) = x 3 is differentiable and its derivative is f′(x) = 3x 2. What does Twice Differentiable Mean? If a function is … WebShow that f is differentiable at x=1, i.e., use the limit definition of the derivative to compute f'(1) . Click HERE to see a detailed solution to problem 9. PROBLEM 10 : Assume that Show that f is differentiable at x=0, i.e., use the limit definition of the derivative to compute f'(0) . Click HERE to see a detailed solution to problem 10. farahnaz forotan
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WebMar 30, 2024 · Transcript [email protected]−(𝑥−1), 𝑥−1<0)┤ = { ((𝑥−1), 𝑥≥[email protected] Show More. Next: Ex 5.2, 10 Important → Ask a doubt . Chapter 5 Class 12 Continuity and Differentiability; Serial order wise; Ex 5.2. Ex 5.2, 1 Ex 5.2, 2 Ex 5.2, 3 ... WebSep 7, 2024 · Let f be a function. The derivative function, denoted by f ′, is the function whose domain consists of those values of x such that the following limit exists: f ′ (x) = … Webx^2 is a parabola centered at the origin....If you take its derivative you get 2x, therefore the derivative of f(x) at 0 would be equal to 0... or you can write as f'(0) = 0....It is a parabola … hmph in japanese