Chapter 2: Q6E (page 77)
Differentiate
\(y = \left( {{e^x} + {\bf{2}}} \right)\left( {{\bf{2}}{e^x} - {\bf{1}}} \right)\)
The derivative of y is \({e^x}\left( {4{e^x} + 3} \right)\).
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
43-45 Find the numbers at which f is discontinuous. At which of these numbers is f continuous from the right, from the left, or neither? Sketch the graph of f.
\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{{x^{\bf{2}}}}&{{\bf{if}}\,\,\,x < - {\bf{1}}}\\x&{{\bf{if}}\,\,\, - {\bf{1}} \le x < {\bf{1}}}\\{\frac{{\bf{1}}}{x}}&{{\bf{if}}\,\,\,x \ge {\bf{1}}}\end{array}} \right.\)
If an equation of the tangent line to the curve \(y = f\left( x \right)\) at the point where \(a = {\bf{2}}\) is \(y = {\bf{4}}x - {\bf{5}}\), find \(f\left( {\bf{2}} \right)\) and \(f'\left( {\bf{2}} \right)\).
Each limit represents the derivative of some function \(f\) at some number \(a\). State such an \(f\) and \(a\) in each case.
\(\mathop {{\rm{lim}}}\limits_{\theta \to \pi /6} \frac{{{\rm{sin}}\theta - \frac{1}{2}}}{{\theta - \frac{\pi }{6}}}\)
19-32 Prove the statement using the \(\varepsilon \), \(\delta \)definition of a limit.
24. \(\mathop {{\bf{lim}}}\limits_{x \to a} c = c\)
19-32: Prove the statement using the \(\varepsilon ,\delta \) definition of a limit.
30. \(\mathop {\lim }\limits_{x \to 2} \left( {{x^2} + 2x - 7} \right) = 1\)
What do you think about this solution?
We value your feedback to improve our textbook solutions.
