Consider the function h(x)= e^ 5x^ 2 +4 for all real numbers .
MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
Consider the function
h(x)=e5x2+4
for all real numbers x.
(a) Calculate x→1limh(x).
(b) Write h explicitly as a composition of three simpler elementary functions. For each component function, indicate the value at which it is evaluated when x=1.
(c) Justify in words why the limit in part (a) can be found by direct substitution, making specific reference to the continuity of each component identified in part (b).