- #1
Miike012
- 1,009
- 0
A function f is defined as follows:
f(x) = 2cos(x) if x≤c,
= ax^2 + b if x > c .
Where a,b, and c are constants. If b and c are given. find all values of a for which f is continuous at the point x = c
Solution:
a = (2cos(c) - b)/c^2 if c ≠ 0 ; if c = 0 there is no solution unless b = 2.
I don't understand how if c = 0 and b = 2 there is a solution at c = 0
For instance... (2cos(c) - 2)/c^2 = (2/c)( Cos(c) - 1 )/c = 2/0*0 as c → 0 which is still a discontinuity.
f(x) = 2cos(x) if x≤c,
= ax^2 + b if x > c .
Where a,b, and c are constants. If b and c are given. find all values of a for which f is continuous at the point x = c
Solution:
a = (2cos(c) - b)/c^2 if c ≠ 0 ; if c = 0 there is no solution unless b = 2.
I don't understand how if c = 0 and b = 2 there is a solution at c = 0
For instance... (2cos(c) - 2)/c^2 = (2/c)( Cos(c) - 1 )/c = 2/0*0 as c → 0 which is still a discontinuity.