Continuity Explained (Limits and Function Values Must Match)

Q) Determine a and b if f(x) is a continuous function, where 𝑓(𝑥)={(2, ≤3 𝑎𝑥+𝑏, 3=𝑥=5 5, 𝑥≥5)

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Q) The value of k for which f(x)={(sin7x/5x,x≠0 k,x=0) is continuous at x=0 is

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Find the values of 𝛌 if the function 𝐟(𝐱)={((〖𝐬𝐢𝐧^𝟐 𝛌𝐱)/𝐱^𝟐 , 𝐢𝐟 𝐱≠𝟎 𝟏, 𝐢𝐟 𝐱=𝟎)

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Q) The value of 𝑘 for which the function 𝑓(𝑥)={(𝑥^2 sin 1/𝑥, 𝑥≠0 𝑘(𝑥+1), 𝑥=0) is a continuo

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