1. Limits and Continuity

Even function limits Suppose f is an even function where lim x→1^− f(x)=5 and lim x→1^+ f(x)=6. Find lim x→−1^− f(x) and limx→−1^+ f(x).

Determine the following limits.

$\underset{z\to 4}{\lim }\frac{z-5}{{(z^2-10z+24)}^2}$

Find the limit: $\underset{t\to 7}{lim}\frac{7+t^2}{7-t^2}$

Determine the following limits.

$\underset{\theta \to 0^{-}}{\lim }\frac{\sin \theta }{{\cos }^2\theta -1}$

Given the function $f\left(x\right)=x$, find the largest value of $\delta$ such that if $|x-4|<\delta |$, then $|x-2|<0.4|$.

Find the limit: $\underset{t\to 5}{lim}\frac{5+t^2}{5-t^2}$

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.

where P(t) is the population, for t ≥ 0, and r > 0 and K > 0 are given constants.

d. Find lim(t→∞) P(t) and check that the result is consistent with the graph in part (c).

Find the arc length of the graph of the function $y=\frac{2}{3}{x}^{\frac{3}{2}}+\frac{1}{3}$ over the interval $0\le x\le 9$.

Find the limit.

$\lim_{x\rarr0}x^3+5x^2-7x+3$

Find the limit.

$\lim_{x\rarr2}\sqrt{x^2+5}$

Find the limit.

$\lim_{x\rarr3}\frac{x^2+2x-3}{x-2}$

Find the limit.

$\lim_{x\rarr0}\frac{3x^2+7x}{x}$

Find the limit.

$\lim_{x\rarr2}\frac{x^2-7x+12}{x-3}$

Find the limit.

$\lim_{x\rarr-2}\frac{x^2-5x-14}{x+2}$

Find the limit.

$\lim_{x\rarr-\pi}\frac{\sin x}{x}$