Calculus Class: Review for Exam 1 (Precalculus Content and Limits)

Go over Quiz 2: intercepts of polynomials, properties of logarithms, amplitude and period of a sinusoidal function, horizontal asymptote for a rational function. Use the inverse sine function (arcsine function) to solve a trigonometric equation. Discuss dominance of functions as x approaches infinity: a power function with a larger power will dominate a power function with a lower power as x goes to infinity, any power function (with positive power) will dominate any logarithmic function as x tends to infinity, and any exponential growth function will dominate any power function as x approaches infinity. Tricky limit calculation example where calculator technology is misleading (numerical error). In the calculation, we must multiply the top and bottom by a conjugate expression of the top (limit conjugate problems). Find a number delta so that if x is within delta units of 4 (between 4 - delta and 4 + delta), then y=x^3 is within epsilon = 0.1 units of 64.

Calculus Class 12, 26 Feb 2021.

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[jackraj]

What can u say about limit existense of 1/Mod(x) . Does it limit exists or not? What would be the plausible answer.. And do share the rationale behind it.