Use continuity to evaluate the limit.
lim
xβ9 16+βx/β16+x
Consider the intervals for...
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Mathematics, 23.02.2021 08:40 gbrightwell
Use continuity to evaluate the limit.
lim
xβ9 16+βx/β16+x
Consider the intervals for which the numerator and the denominator are continuous.
The numerator 16+βx
is continuous on the interval Correct The denominator β16+x is continuous and nonzero on the interval
The interval for which the quotient is continuous is the intersection of the above intervals. Therefore, the quotient 16+βx/β16+x is continuous on the interval
Since x=9 is in the interval [0,β) , then f is continuous at x=9 . Therefore, limxβ9
16+βx/β16+x=f(9)=
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