Calculus, 5th Edition solutions

Calculus, 5
(a) By comparing areas, show that 5. (b) Use the Midpoint Rule with to estimate .

Calculus, 5
Refer to Example 1. (a) Find the equation of the tangent line to the curve that is parallel to the secant line . (b) Use part (a) to show that ln 2 0.66.

Calculus, 5
By comparing areas, show that 12131n ln n 1 12131n  13

Calculus, 5
(a) By comparing areas, show that . (b) Deduce that . 2 e 3 l

Calculus, 5
Prove the third law of logarithms. [Hint: Start by showing that both sides of the equation have the same derivative.]

Calculus, 5
Prove the second law of exponents for [see (11)].

Calculus, 5
Prove the third law of exponents for [see (11)].

Calculus, 5
Prove the second law of exponents [see (15)].

Calculus, 5
Prove the fourth law of exponents [see (15)].

Calculus, 5
Deduce the following laws of logarithms from (15): (a) (b) (c) logax y y loga x logaxy loga x  loga y logaxy loga x  loga y ex ex