Recommended Books on Amazon (affiliate links) | ||
---|---|---|
Join Amazon Student - FREE Two-Day Shipping for College Students |
We will be adding more discussion here soon. In the meantime, enjoy these practice problems.
Practice
Find the equation of the tangent plane and the symmetric equations of the normal line to the surface \( 2(x-2)^2 + (y-1)^2 + (x-3)^2 = 10 \) at the point \( (3,3,5) \).
Problem Statement |
---|
Find the equation of the tangent plane and the symmetric equations of the normal line to the surface \( 2(x-2)^2 + (y-1)^2 + (x-3)^2 = 10 \) at the point \( (3,3,5) \).
Solution |
---|
video by Krista King Math |
---|
Log in to rate this practice problem and to see it's current rating. |
---|
Determine the equation of the line that passes through the point \( (1,-1,1) \) and is normal to the plane \( 2x + 3y - z = 4 \).
Problem Statement |
---|
Determine the equation of the line that passes through the point \( (1,-1,1) \) and is normal to the plane \( 2x + 3y - z = 4 \).
Solution |
---|
video by Dr Chris Tisdell |
---|
Log in to rate this practice problem and to see it's current rating. |
---|
Determine a normal vector and the equation of the tangent plane to the surface \( z = x^2 + 2y^2 \) at the point \( A(2,-1,6) \).
Problem Statement |
---|
Determine a normal vector and the equation of the tangent plane to the surface \( z = x^2 + 2y^2 \) at the point \( A(2,-1,6) \).
Solution |
---|
video by Dr Chris Tisdell |
---|
Log in to rate this practice problem and to see it's current rating. |
---|
Find the tangent plane to the surface \( x=u^2, y=u-v^2, z=v^2 \) for \( u,v \geq 0 \) at the point \((1,0,1)\).
Problem Statement |
---|
Find the tangent plane to the surface \( x=u^2, y=u-v^2, z=v^2 \) for \( u,v \geq 0 \) at the point \((1,0,1)\).
Solution |
---|
video by Michael Hutchings |
---|
Log in to rate this practice problem and to see it's current rating. |
---|
Really UNDERSTAND Calculus
external links you may find helpful |
---|
The Unit Circle
The Unit Circle [wikipedia]
Basic Trig Identities
Set 1 - basic identities | |||
---|---|---|---|
\(\displaystyle{ \tan(t) = \frac{\sin(t)}{\cos(t)} }\) |
\(\displaystyle{ \cot(t) = \frac{\cos(t)}{\sin(t)} }\) |
\(\displaystyle{ \sec(t) = \frac{1}{\cos(t)} }\) |
\(\displaystyle{ \csc(t) = \frac{1}{\sin(t)} }\) |
Set 2 - squared identities | ||
---|---|---|
\( \sin^2t + \cos^2t = 1\) |
\( 1 + \tan^2t = \sec^2t\) |
\( 1 + \cot^2t = \csc^2t\) |
Set 3 - double-angle formulas | |
---|---|
\( \sin(2t) = 2\sin(t)\cos(t)\) |
\(\displaystyle{ \cos(2t) = \cos^2(t) - \sin^2(t) }\) |
Set 4 - half-angle formulas | |
---|---|
\(\displaystyle{ \sin^2(t) = \frac{1-\cos(2t)}{2} }\) |
\(\displaystyle{ \cos^2(t) = \frac{1+\cos(2t)}{2} }\) |
Trig Derivatives
\(\displaystyle{ \frac{d[\sin(t)]}{dt} = \cos(t) }\) |
\(\displaystyle{ \frac{d[\cos(t)]}{dt} = -\sin(t) }\) | |
\(\displaystyle{ \frac{d[\tan(t)]}{dt} = \sec^2(t) }\) |
\(\displaystyle{ \frac{d[\cot(t)]}{dt} = -\csc^2(t) }\) | |
\(\displaystyle{ \frac{d[\sec(t)]}{dt} = \sec(t)\tan(t) }\) |
\(\displaystyle{ \frac{d[\csc(t)]}{dt} = -\csc(t)\cot(t) }\) |
Inverse Trig Derivatives
\(\displaystyle{ \frac{d[\arcsin(t)]}{dt} = \frac{1}{\sqrt{1-t^2}} }\) |
\(\displaystyle{ \frac{d[\arccos(t)]}{dt} = -\frac{1}{\sqrt{1-t^2}} }\) | |
\(\displaystyle{ \frac{d[\arctan(t)]}{dt} = \frac{1}{1+t^2} }\) |
\(\displaystyle{ \frac{d[\arccot(t)]}{dt} = -\frac{1}{1+t^2} }\) | |
\(\displaystyle{ \frac{d[\arcsec(t)]}{dt} = \frac{1}{\abs{t}\sqrt{t^2 -1}} }\) |
\(\displaystyle{ \frac{d[\arccsc(t)]}{dt} = -\frac{1}{\abs{t}\sqrt{t^2 -1}} }\) |
Trig Integrals
\(\int{\sin(x)~dx} = -\cos(x)+C\) |
\(\int{\cos(x)~dx} = \sin(x)+C\) | |
\(\int{\tan(x)~dx} = -\ln\abs{\cos(x)}+C\) |
\(\int{\cot(x)~dx} = \ln\abs{\sin(x)}+C\) | |
\(\int{\sec(x)~dx} = \) \( \ln\abs{\sec(x)+\tan(x)}+C\) |
\(\int{\csc(x)~dx} = \) \( -\ln\abs{\csc(x)+\cot(x)}+C\) |
To bookmark this page and practice problems, log in to your account or set up a free account.
Do you have a practice problem number but do not know on which page it is found? If so, enter the number below and click 'page' to go to the page on which it is found or click 'practice' to be taken to the practice problem.
| |