Q44 of 155 Page 9

Let . If f(x) is continuous at
 find a and b.

Given:


f(x) is continuous at x = & f() = a,


If f(x) to be continuous at x = ,we have to show, f()– = f() + = f()


LHL = f()– =



sin(–x) = cosx


cos(–x) = sinx





(a3–b3) = (a–b)(a2 + ab + b2)






∴ cos(0) = 1




...(1)


LHL = f() + =











1


...(2)


f(x) is continuous at x = & f() = a ,and from (1) & (2),we get


f()– = f() + = f()


= a


a =



⇒ b = 4


Hence ,a = & b = 4


More from this chapter

All 155 →
42

For what value of is the function continuous at x = 0? What about continuity at x = ± 1?

 43

For what value of k is the following function continuous at x = 2?

 45

If the function f(x), defined below is continuous at x = 0, find the value of k:

 46

Find the relationship between ‘a’ and ‘b’ so that the function ‘f’ defined by is continuous at x = 3.