The table below gives values of a continuous function for several large positive inputs

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

The table below gives values of a continuous function

f

for several large positive inputs.

$x$	$50$	$100$	$200$	$400$	$800$
$f(x)$	$3.020$	$3.010$	$3.005$	$3.0025$	$3.00125$

Use the table to investigate the end behavior of

f

. (a) Estimate

\displaystyle \lim_{x\to\infty} f(x)

, accurate to three decimal places. Show how the data support your estimate. (b) State the equation of any horizontal asymptote suggested by part (a). Include a brief justification based on the numerical evidence.

Related theory

Limits
Limits of algebraic functions
Limits and Continuity

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