Mathematics

Problem

Consider the function

h(x)=\sqrt{e^{5x^{2}}+4}

for all real numbers

x

. (a) Calculate

\displaystyle \lim_{x\to1} h(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).

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