Question 1

Find dy/dx by implicit differentiation.  &#10;

Accepted Answer

11ea8a3b_b6d5_7f7a_9fff_e733ade9a428_TB6897_11

Question 2

Calculate   &#10; &#10;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E) none of these

Accepted Answer

To add the two values, we can simply add each corresponding digit in hexadecimal system. Starting from the rightmost digit, 7+0=7, 1+6=7, 9+1=10, which we write as 0 carry 1, f+f=e carry 1, and so on. Finally, we get 11ea8a3b_b6d5_0a3e_9fff_0fbb5c3f2853_TB6897_11.

Question 3

Find the tangent line to the ellipse   at the point  &#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E) none of these

Accepted Answer

The equation for the ellipse is:
$\frac{(x-11ea8a3b\_b6d5\_3156\_9fff\_242578040c7e\_TB6897\_11)^2}{225}+\frac{(y-11ea8a3b\_b6d5\_3156\_9fff\_9e1eb4d4f0dd\_TB6897\_11)^2}{36}=1$
At the point $A(11ea8a3b\_b6d5\_3153\_9fff\_53c06fcad59f\_TB6897\_11)$ :
$A(191,33)$
The derivative of the ellipse at point A gives the slope of the tangent line
$-\frac{225(y-A_y)}{36(x-A_x)}$
Evaluating this at point A:
$-\frac{225(y-33)}{36(x-191)}=-\frac{25}{3(x-191)}(y-33)$ 
Plugging in point A the equation for the tangent line becomes:
$y=-\frac{25}{3(x-191)}(y-33)+33$
$y=-\frac{25}{3(x-191)-3}+33$
$y=-\frac{25}{3}(x-191)+33	imes 4$
Simplifying:
$y=-\frac{25}{3}x+229$
Thus, the answer is C) 11ea8a3b\_b6d5\_5866\_9fff\_79755cd5cb74\_TB6897\_11.

Question 4

The curve with the equation   is called an asteroid.Find an equation of the tangent to the curve at the point (   ,1).  &#10;

Accepted Answer

The answer of The curve with the equation  ...

Question 5

Find an equation of the tangent line to the given curve at the indicated point.    &#10;

Accepted Answer

The answer of Find an equation of the tangent line...

Deck 2: Extension F: Limits and Derivatives