Math

h2o
h.w11.docx

 Discuss on the forum. No need to submit. Find

where
= g(x)
.

 Discuss on the forum. But do not submit. Find

/dx (x^2 y)
where
= g(x)
.

 Find

/dx (sin y+y cos x)
where
= g(x)
.

 Find

y/dx
by implicit differentiation.
oot(x)-root(y) = 8
.

 Find

x/dt
by implicit differentiation.
-root(t) = t x
.

 Find

y/dx
by implicit differentiation.
oot (x y)+x y^2 = 4
. [very long]

 Find

y/dx |_(x = 3, y = 2)
by implicit differentiation of
^4+y^4 = 97
. What is the geometric meaning of
y/dx |_(x = 3, y = 2)
?

 Find an equation of the tangent line to the circle:

^2+y^2 = 25
at the point
-3, 4)
. Then graph the line together with the circle. In order to graph equations, you need to solve them for
http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7By%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15
. To graph
^2+y^2 = 25
, plot
= root (25-x^2)
and
=-root (25-x^2)
.

 Find an equation of the tangent line to the astroid:

x^(2))^(1/3)+(y^(2))^(1/3) = 4
at the point
-3 root(3),1)
.

ttp://calculus.sfsu.edu/latexrender/pictures/824746d028384b64bd93ba0a49a8ec7a.png

 Find an equation of the tangent line to the hyperbola:

^(2)-2 y^(2) = 1
at the point
a,b)
.

ttp://calculus.sfsu.edu/latexrender/pictures/4e5fc4c5dda366a7e6e1205ecd4b5724.png

 Do not submit but please discuss it .You may earn valuable participation points. Using the theorem about the derivative of an inverse, show that for positive integers

http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7Bm%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15
and
> 0
,
(x)^(1/m))' = 1/m x^(1/m-1).

 Do not submit but please discuss it Nairobi and Rio are located on the Tropic of Capricorn. On December 21, that is on the day of the Solstice at midday the Sun is vertical. How fast is the shadow of a pole 3 meters tall increasing at (a) midday, (b) at dusk?