Areas and Logarithms

abscissas accuracy ak+1 altitudes approaches zero approximation arbitrarily area of ACDB assume base becomes bk+1 booklet bounded calculating called Chebyshev compute Consequently consider correct corresponding curve curvilinear trapezoid curvilinear trapezoid ACDB curvilinear triangle deduced defined definition denote difference divide draw equal error error less example exponent expression fact formula function geometric progression given gives graph greater height Hence holds increases integral length Let us take letter lies limit linear logarithmic curve lower mathematical means method move natural logarithms necessary negative observe obtain Obviously path positive problem properties prove ratio rectangle relation remains represented result rises segment side smaller step-like figure steps sufficiently term tion unit University upper valid whole x-axis y-axis