Find the limit by creating a table of values.
$\(\lim\)_{x\(\rarr\)0}-4x+2$

Find the exact length of the curve $y=\ln (1-x^2)$ for $0\le x\le \frac{1}{3}$.

63–66. Calculator limits Use a calculator to make a table similar to Table 7.1 to approximate the following limits. Confirm your result with l’Hôpital’s Rule.

limₕ→₀ (1 + 2h)^{1/h}

63–66. Calculator limits Use a calculator to make a table similar to Table 7.1 to approximate the following limits. Confirm your result with l’Hôpital’s Rule.

limₕ→₀ (1 + 3h)^{2/h}

52-56. In this section, several models are presented and the solution of the associated differential equation is given. Later in the chapter, we present methods for solving these differential equations.

{Use of Tech} Free fall One possible model that describes the free fall of an object in a gravitational field subject to air resistance uses the equation v'(t) = g - bv, where v(t) is the velocity of the object for t ≥ 0, g = 9.8 m/s² is the acceleration due to gravity, and b > 0 is a constant that involves the mass of the object and the air resistance.

c. Using the graph in part (b), estimate the terminal velocity lim(t→∞) v(t).

Find the limit by creating a table of values.

$\(\lim\)_{x\(\rarr\)2}3x^2+5x+1$

Find the limit by creating a table of values.

$\(\lim\)_{x\(\rarr\)1}\(\frac{x^2-4}{x-2}\)$

Find the limit using the graph of $f\(\left\)(x\(\right\))$shown.

$\(\lim\)_{x\(\rarr\)1}f\(\left\)(x\(\right\))$

Find the limit using the graph of $f\(\left\)(x\(\right\))$shown.

$\(\lim\)_{x\(\rarr\)-2}f\(\left\)(x\(\right\))$