Linear Approximation and Differentials Worksheet with Answer Key

What's on the worksheet

1. Find the linearization $L
   f(x) = e^{3x}, \; a = 0f(x) = \sqrt{x}, \; a = 9f(x) = \ln x, \; a = ef(x) = \sin x, \; a = \dfrac{\pi}{6}
2. Write the differential dy for each function.
   y = x^2 e^xy = \ln(x^2 + 1)y = \sqrt{1 - x^2}y = \tan 3x
3. Use a linearization of $f
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