At what point do the curves $r_1\left(t\right)=(t,2-t,35+t^2)$ and $r_2\left(s\right)=(7-s,s-5,s^2)$ intersect?

Additional Graphing Exercises

[Technology Exercise] Graph the curves in Exercises 109–112. Explain the relationship between the curve’s formula and what you see.

y = −1 / √(4 − x²)

Finding Limits of Differences When x → ±∞

Find the limits in Exercises 84–90. (Hint: Try multiplying and dividing by the conjugate.)

lim x → ∞ (√(x² + 25) − √(x² − 1))

Given the function $f\left(x\right)=2x^2-3x+1$, which of the following is the average rate of change of $f\left(x\right)$ over the interval from $x=-6$ to $x=-3$?

How many tangent lines to the curve $y=\frac{x}{x+1}$ pass through the point $(1,\frac{1}{2})$?

Given that $d\left(t\right)$ is a known function and $d$ is a specific value, which of the following procedures will find the time $t$ at which $d\left(t\right)=d$?

Find the exact length of the curve $y=x-x^2+{\sin -1}^x$ from $x=0$ to $x=1$.

Given that $\underset{x\to 1}{lim}f\left(x\right)=1$, find the largest value of $\epsilon >0$ such that if $|x-1|<\delta$, then $\left|f\right(x)-1|<0.2$. Which of the following values of $\delta$ satisfies this condition?

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