True/False. If $\mathbf{f}: \mathbf{R}^{3} \rightarrow \mathbf{R}^{4}$ is differentiable, then Df(x) is a $3 \times 4$ matrix.

$\triangle A B C \sim \triangle F D E$. What is DE?

Given that the length of $\overline{AC}=12$, $\overline{BC}=8$, $\overline{EF}=18$, and $\overline{DF}=6$

Solve the equation or formula for the variable indicated.

$$\frac{df + 10}{6} = g,\ for\ f$$

Given f(x) = 2x+3, a = -1: (a) Find f^{-1}(x). (b) Graph f and f^{-1} together. (c) Evaluate df/dx at x = a and df^{-1}/dx at x = f(a) to show that at these points df^{-1}/dx = 1/(df/dx).

Let f(x)=x^3-3 x^2-1, $x \geq 2$ Find the value of df^{-1} / dx at the point x=-1=f(3)

Suppose that the differentiable function y=f(x) has an inverse and that the graph of f passes through the point (2,4) and has a slope of 1/3 there. Find the value of df^{-1} / dx at x=4.

In $\triangle \mathrm { DEF } ,$ find $\angle \mathrm { F }$ to the nearest degree, if $\mathrm { DE } = 15 \mathrm { cm } , \mathrm { DF } = 18 \mathrm { cm } , \text { and } \angle \mathrm { E } = 90 ^ { \circ }$

Find the following ratio $\triangle D E F$ where $m \angle E$ = $90^\circ$ DE = 4, EF= 3, DF = 5.

$$\sin F$$

Find df/dx if

$$f(x)=\int_1^{e^x} \frac{2 \ln t}{t} d t$$

If a parallelepiped with sides $\overline{DE}, \overline{DF}$, and $\overline{DG}$ has "7ero volume." what can you say about points D, E,F and $G$ ?

Consider an F-curve with df=(2, 14). Find the F -value with area 0.05 to its right.

Given f(x) = 5-4x, a = 1/2: (a) Find f^{-1}(x). (b) Graph f and f^{-1} together. (c) Evaluate df/dx at x = a and df^{-1}/dx at x = f(a) to show that at these points df^{-1}/dx = 1/(df/dx).

Given f(x) = 2x^2, $x\geq 0$, a = 5: (a) Find f^{-1}(x). (b) Graph f and f^{-1} together. (c) Evaluate df/dx at x = a and df^{-1}/dx at x = f(a) to show that at these points df^{-1}/dx = 1/(df/dx).

Find the following ratio $\triangle D E F$ where $m \angle E$ = $90^\circ$ DE = 4, EF= 3, DF = 5.

$$\tan D$$