Calculus 1 : Calculus
Study concepts, example questions & explanations for Calculus 1
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Example Questions
Example Question #891 : Spatial Calculus
Find a vector perpendicular to 
By definition, any vector 
We can verify this further by noting that the product of any vector 
Example Question #892 : Spatial Calculus
Find a vector perpendicular to 
By definition, any vector 
We can verify this further by noting that the product of any vector 
Example Question #7 : Integration
If the velocity function of a car is 
To find the position from the velocity function, take the integral of the velocity function.
Substitute 
Example Question #893 : Spatial Calculus
For this question, remember that velocity is 
A particle's velocity is given by the function 
Position is the anti-derivative of velocity, so we find the anti-derivative of the given velocity function to find the position function.
The velocity function is given as 
We then evaluate that function at the given point 
Example Question #41 : Position
Which of the following is perpendicular to the vector 
By definition, a given vector 
Since we are given a vector 
Perpendicular vectors have a dot product of zero therefore,
Example Question #42 : Position
Which of the following is perpendicular to the vector 
By definition, a given vector 
Perpendicular vectors have a dot product of zero therefore,
Plugging in our values, we can verify the two vectors are perpendicular.
Example Question #43 : Position
Which of the following is perpendicular to the vector 
By definition, a given vector 
Perpendicular vectors have a dot product of zero therefore,
Plugging in our values, we can verify the two vectors are perpendicular.
Example Question #41 : How To Find Position
Harold is sitting in a parked car 10 feet from a wall. He begins to accelerate the car at a rate of 14 feet per second squared away from the wall. How far away from the wall will he be in 6 seconds?
To begin, let's recognize that since acceleration is the second derivative of position with respect to time, we can in turn, integrate an acceleration function twice with respect to time to find position.
Since accleration is a constant, 14 feet per second, our acceleration function is:
Integrating this once gives us a velocity function
where
is our initial velocity. Since the car started at rest, v0 will be equal to zero, leaving us with:
To get our position function, we can in turn integrate our velocity function:
where x0 is our initial position. We are told that our initial position is 10 feet away from the wall, so we can rewrite this equation as:
To find where the car is at 6 seconds, we need only plug in the value of 6 seconds where ever our time variable t occurs, giving our answer of 262 feet.
Example Question #45 : Position
Which of the following vectors is perpendicular to 
By definition, a given vector 
To verify that two vectors are perpendicular their dot product must equal zero.
The dot product is as follows.
Substituting in our vector values we get:
Example Question #892 : Spatial Calculus
Which of the following vectors is perpendicular to 
By definition, a given vector 
To verify that two vectors are perpendicular their dot product must equal zero.
The dot product is as follows.
Substituting in our vector values we get:
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