Find #a# and #b# so that # f(x) = { (x^2, xle1),(ax+b,x gt 1) :} # is continuous?
1 Answer
Mar 27, 2017
# a=1-b #
Explanation:
We have:
# f(x) = { (x^2, xle1),(ax+b,x gt 1) :} #
Both
In order for continuity at
# lim_(x rarr 1) f(x) = f(1) #
Consider the LH limit;
# lim_(x rarr 1^-) f(x) = lim_(x rarr 1^-) x^2 = 1#
And the RH limit:
# lim_(x rarr 1^+) f(x) = lim_(x rarr 1^+) ax+b =a+b#
So the requirement for continuity is:
# lim_(x rarr 1^-) f(x) = lim_(x rarr 1^+) f(x) #
# :. a+b =1 => a=1-b #