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

$$\sin D$$

What does $df$ stand for in stats?

Use $\triangle G H J$, where D, E, and F are midpoints of the sides.

If HJ=8x-2 and DF=2x+11, what is HJ?

Consider an F-curve with df=(2, 14). Find the F -va1ue with area 0.01 to its right.

If in $\triangle \mathrm{A B C}$ and $\triangle \mathrm{D E F}$, AB = DE, $\mathrm{m} \angle \mathrm{A B C=\mathrm{m} \angle E D F}$, BC = DF, $\mathrm{A C}=(20 x-10)$, and $\mathrm{E F}=(15 x+15)$, what is the value of x?

Find df/dx if

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

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

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

$$\sin F$$

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

$$\cos D$$

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)

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).

Perform the operation : $DF$, where matrices $A$ and $C$ are :

$$D= \begin{bmatrix} 3 & 0\\ 1 & -1 \\ 2 & 5 \end{bmatrix} \ \ \ \ F= \begin{bmatrix} 1 \\ 0 \\ -1 \end{bmatrix}$$

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

Let f(x)=x^2-4x-5, x>2 . Find the value of df^{-1} / dx at the point x=0=f(5).