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Theorems for Continuity

If f x =sin...

Question

If $f (x) = \frac{sin 4 x}{5 x} + a, f o r x > 0$
$= x + 4 - b f o r x < 0$
$= 1 f o r x = 0$ is continuous
at x=0, find a and b.

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Solution

Since f(x) is continuous at x=0
1=0+4-b= $l i m_{x \to 0} \frac{s i n 4 x}{5 x} + a$
1=4-b= $\frac{4}{5} + a$ which gives b=3 and a= $\frac{1}{5}$

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