Let f(x) = tan(x²) and g(x) = x|x| for |x|

Question

Let f(x) = tan(x²) and g(x) = x|x| for |x| < √(π/2). If q(x) = f∘g(x), then which of the following statements is/are correct? I. q(x) is continuous at x = 0. II. q(x) is differentiable at x = 0. Select the answer using the code given below:

Accepted Answer

Both I and II. q(x) = f(g(x)) = tan((x|x|)²) = tan(x²·x²) = tan(x⁴). This is continuous at x = 0 with value 0. Its derivative q'(x) = 4x³·sec²(x⁴), so q'(0) = 0 exists. Hence both continuous and differentiable at x = 0.

Let f(x) = tan(x²) and g(x) = x|x| for |x| < √(π/2). If q(x) = f∘g(x), then which of the following statements is/are correct? I. q(x) is continuous at x = 0. II. q(x) is differentiable at x = 0. Select the answer using the code given below:

Explanation

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