BC Calculus Assignment 36: Exponentials Worksheet B
Class: 5H: BC Calculus
Author: Peter Atlas
Text:
Calculus
Finney, Demana, Waits, Kennedy
Use the fact that \(y = \ln {x}\) and \(y = e^x\) are inverses of each other to simplify the following expressions:
\( e^{\ln {7}} \)
Solution
7
\( e^{3 \ln {2 }}\)
Solution
8
\( e^{-2 \ln {3 }}\)
Solution
\(\frac{1}{9}\)
\( e^{2 + \ln {3 }}\)
Solution
\(3e^2\)
Solve the following for \(y\).
\( \ln {y} = 2t + 4 \)
Solution
\(y = e^{2t + 4}\)
\( \ln {(1 - 2y)} = t \)
Solution
\( y = \frac{e^t - 1}{ -2} \)
\( 5 + \ln {y} = 2 ^{x^2 + 1} \)
Solution
\( y = e^{2^{x^2 + 1} - 5} \)
\( \ln {(2^y - 1)} = x^2 - 3 \)
Solution
\( y = \frac{ \ln{ \left( e^{x^2 - 3} + 1 \right) }}{\ln{2}}\)
Find \( \frac{dy}{dx} \).
\( y = 2e^x \)
Solution
\( y' = 2e^x \)
\( y = e^{-\frac{x}{4}} \)
Solution
\( y' = -\frac{1}{4} e^{-\frac{x}{4}} \)
\( y = x^2e^x - xe^x \)
Solution
\( y' = e^x(x^2 + x - 1) \)
\( y = e^{x^2} \)
Solution
\( y' = 2xe^{x^2} \)