Determine values of a and b that make the given function continuous. f(x) = { 59sin(x) / x if x < 0 a if x = 0 bcos(x) if x > 0 a = [ ] and b = [ ]

          Determine values of a and b that make the given function continuous.
f(x) = {
59sin(x) / x if x < 0
a if x = 0
bcos(x) if x > 0
a = [ ] and b = [ ]

Added by James C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

11/27/2023

Step 1

As x approaches 0 from the left, we have: $$\lim_{x \to 0^-} 59\sin(x)$$ Since the sine function is continuous, we can plug in 0: $$59\sin(0) = 59 \cdot 0 = 0$$ Now, as x approaches 0 from the right, we have: $$\lim_{x \to 0^+} b\cos(x)$$ Since the cosine Show more…

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