For the function f(x) = sin(5x)/x for x ≠ 0, and f(0) = k. If f(x) is continuous at x = 0, find k. A. 0 B. 1 C. 5 D. 1/5 Answer: C) 5 Explanation: lim(x→0) sin(5x)/x. Multiply and divide by 5 to get 5 × lim(x→0) sin(5x)/(5x) = 5 × 1 = 5. For continuity, f(0) must equal 5.

imo class 12 continuity and differentiability

For the function f(x) = sin(5x)/x for x ≠ 0, and f(0) = k. If f(x) is continuous at x = 0, find k.

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For the function f(x) = sin(5x)/x for x ≠ 0, and f(0) = k. If f(x) is continuous at x = 0, find k.

Answer: C) 5

Explanation: lim(x→0) sin(5x)/x. Multiply and divide by 5 to get 5 × lim(x→0) sin(5x)/(5x) = 5 × 1 = 5. For continuity, f(0) must equal 5.