Find the radius of curvature of y=ln(x+1) at point (2, ln3).

Which of the following is not a problem associated with deforestation? (a) Loss of habitat for plants and animals, (b) Increased soil erosion, (c) Changes in the local climate, (d) Destruction of old farms and ranches.

At what point does the curve $y = e ^ { x }$ have maximum curvature?

How does commercial paper differ from a bank loan? Why is the interest rate often less for commercial paper?

Find equations of the normal plane and osculating plane of the curve at the given point.

$$x=t, y=t^2, z=t^3; (1, 1, 1)$$

What happens to the curvature as $x \rightarrow \infty$ for the curve $y = e ^ { x }$?

Suppose you roll two four-sided dice, numbered from 1 to 4. a. What is the most likely sum of the dice? b. What is the probability that the dice will total 7?

A school offered an optional, free SAT prep class for juniors. Students could choose whether to attend the class. Juniors who took the class, on average, scored 300 points higher on the SAT than their classmates who did not attend the class. The principal says this proves the class is very successful and should be offered again next year. a. State at least one reason the principal might be wrong about the class. b. State one way enrollment in the SAT prep class could have been changed to provide a better measurement of the relationship between taking the SAT prep class and a student's score on the SAT.

Evaluate the following integrals: $\int_{0}^{1} \mathbf{r}(t) d t$, where $\mathbf{r}(t)=\left\langle\sqrt[3]{t}, \frac{1}{t+1}, e^{-t}\right\rangle$

Find the curvature K of the curve at the point P. r(t) = ti + t²j + t³/4 k, P(2, 4, 2)

Evaluate the following integrals: $\int \left( e ^ { t } \mathbf { i } + \sin t \mathbf { j } + \frac { 1 } { 2 t - 1 } \mathbf { k } \right) d t$

Find the curvature K of the curve at the point P. r(t) = e^t cos ti + e^t sin tj + e^t k, P(1, 0, 1)

Find equations of the osculating circles of the ellipse

$$9x^2+4y^2=36$$

at the points (2, 0) and (0, 3). Use a graphing calculator or computer to graph the ellipse and both osculating circles on the same screen.

Find the unit tangent vector $\mathbf{T}(\mathrm{t})$ for the following vector valued functions. $\mathbf{r}(t)=\langle t+1,2 t+1,2 t+2\rangle$