Let f(x) = cases x 1 x , & x 0 0, & x = 0 cases and g(x) = cases x^2 1 x , & x 0 0, &…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let f(x)={xsin⁡1x,x≠00,x=0f(x) = \begin{cases} x \sin \frac{1}{x}, & x \neq 0 \\ 0, & x = 0 \end{cases} and g(x)={x2sin⁡1x,x≠00,x=0g(x) = \begin{cases} x^2 \sin \frac{1}{x}, & x \neq 0 \\ 0, & x = 0 \end{cases} Discuss the graph for f(x)f(x) and g(x)g(x), and evaluate the continuity and differentiability of f(x)f(x) and g(x)g(x).

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