Ex 5.1, 23 - Find all points of discontinuity of f(x) = {sinx/x - Checking continuity using LHL and RHL

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Ex 5.1, 23 Find all points of discontinuity of f, where 𝑓(π‘₯)={β–ˆ(𝑠𝑖𝑛π‘₯/π‘₯, 𝑖𝑓 π‘₯<0@&π‘₯+1, 𝑖𝑓 π‘₯β‰₯0)─ 𝑓(π‘₯)={β–ˆ(𝑠𝑖𝑛π‘₯/π‘₯, 𝑖𝑓 π‘₯<0@&π‘₯+1, 𝑖𝑓 π‘₯β‰₯0)─ Case 1: At x = 0 A function is continuous at x = 0 if L.H.L = R.H.L = 𝑓(0) i.e. lim┬(xβ†’0^βˆ’ ) 𝑓(π‘₯) = lim┬(xβ†’0^+ ) 𝑓(π‘₯) = 𝑓(0) Thus, f is continuous for all real numbers ∴ There is no point of discontinuity

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