Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
Stewart_Calc_7ET ch03sec05
MULTIPLE CHOICE
1. Find the tangent line to the ellipse at the point .
a.
b.
c.
d.
e.
2. Use implicit differentiation to find an equation of the tangent line to the curve at the given
point.
a.
b.
c.
d.
e.
3. Find dy/dx by implicit differentiation.
a.
b.
c.
d.
4. Find dy/dx by implicit differentiation.
a.
b.
c.
d.
5. Use implicit differentiation to find an equation of the tangent line to the curve at the
indicated point.
y = sin xy6;
a.
x =
b.
y = 6x + 1
c.
y = x
d.
y = 1
6. Find in terms of x and y.
a.
b.
c.
d.
7. Find in terms of x and y.
a.
b.
c.
d.
8. Calculate .
a.
b.
c.
d.
e.
none of these
9. If , find .
a.
b.
c.
d.
e.
10. If and , find when .
a.
b.
c.
d.
e.
None of these
11. Find the derivative of the function.
a.
b.
c.
d.
e.
12. Find an equation of the tangent line to the curve at the point
(4,1).
a.
b.
c.
d.
e.
MULTIPLE RESPONSE
1. Find equations of the tangent lines to the curve that are parallel to the line
.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. Calculate .
2. Calculate .
3. Calculate .
4. Find by implicit differentiation.
SHORT ANSWER
1. Find dy/dx by implicit differentiation.
2. Find the rate of change of y with respect to x at the given values of x and y.
; x = 3, y = –5
3. Find an equation of the tangent line to the curve
at (1, 0).
4. Find the derivative of the function.
5. Find an equation of the tangent line to the given curve at the indicated point.
6. The curve with the equation is called an asteroid. Find an equation of the
tangent to the curve at the point ( , 1).
7. Two curves are said to be orthogonal if their tangent lines are perpendicular at each point of
intersection of the curves. Show that the curves of the given equations are orthogonal.
1–1 x
2
4
–2
–4
y
3 3
08–8
8
–8
x
y
y – x = x = cos y
3
4
3
4
123–1–2–3 x
1
2
3
–1
–2
–3
y
