Ex 5.1, 17
Last updated at Dec. 8, 2016 by Teachoo
Transcript
Ex 5.1, 17 Find the relationship between a and b so that the function f defined by 𝑓 𝑥= 𝑎𝑥+1, 𝑖𝑓 𝑥≤3&𝑏𝑥+3, 𝑖𝑓 𝑥>3 is continuous at x = 3. Given 𝑓 𝑥= 𝑎𝑥+1, 𝑖𝑓 𝑥≤3&𝑏𝑥+3, 𝑖𝑓 𝑥>3 Given function is continuous at x = 3 f is continuous at x = 3 if L.H.L = R.H.L = 𝑓 3 i.e. if limx→ 3− 𝑓 𝑥 = limx→ 3+ 𝑓 𝑥 = 𝑓 1 And 𝑓 𝑥=ax+1 So, 𝑓 3=3a +1 Now, limx→ 3− 𝑓 𝑥 = limx→ 3+ 𝑓 𝑥 = 𝑓 1 3𝑎 + 1 = 3𝑏 + 3 = 3𝑎 + 1 ⇒ 3𝑎 + 1 = 3𝑏 + 3 ⇒ 3𝑎−3b=3−1 ⇒ 3𝑎 −3𝑏=2 ⇒ 3 𝑎−𝑏=2 ⇒ 𝑎−𝑏= 23 ⇒ 𝑎=𝑏+ 23 Thus , for any arbitrary value of b. We can find value of a.
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About the Author
CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .