Calculus 1 : Equations
Study concepts, example questions & explanations for Calculus 1
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Example Questions
Example Question #2291 : Calculus
Find the equation of the line tangent to 
The tangent line does not exist at this point.
To find the equation for the tangent line, we must first find the derivative of 
In order to evaluate this derivative, we must use these formulae:
Next we find the slope of the tangent line at this point:
Then we need to plug the given 
Now that we have a point 
So, the equation for the line is 
Example Question #211 : Equations
Give the position equation 
For this equation, let's start with acceleration and move backwards towards position. We know that the object is accelerating at a constant rate of
To solve for velocity , we integrate both sides with respect to
Since we know that the initial velocity is 
To solve for position we have to take the integral of both sides with respect to 
Since we know that the initial position is 
The formula for this motion can be modelled by:
Example Question #1261 : Functions
Inverse Function
What is the inverse function of the following:
None of the above
Example Question #1262 : Functions
Logarithm Functions
Solve for 
Example Question #212 : Equations
Write the integral expression for how to find the area under the curve 
To write the expression, simply use the bounds laid out by the x-coordinates of the points given. Thus, your answer is:
Example Question #21 : How To Write Equations
For what values of the constant 
Both 
Example Question #212 : Equations
White the expression for the derivative of the following function.
To solve, simply differentiate and don't forget to indicate the differentiation by the "apostrophe" between the function and dependent variable. Thus,
Example Question #23 : How To Write Equations
Find the equation for the velocity whose position function is below:
To solve, simply differentiate 
Remember to use the power rule.
Recall the power rule:
Apply this to our situation to get
Example Question #31 : Other Writing Equations
Find the second derivative of the following function:
The second derivative is the derivative of the first derivative function.
With our original function,
We may find the first derivative to be:
Note that the chain rule was used to find the first derivative.
Now to find the second derivative we must take the derivative of this function:
Example Question #31 : How To Write Equations
You wish to find the area under the line 
To find the area under a curve, you need to use an integral expression. The number at the base of your integral sign is your lower bound (the smaller x-value that defines one vertical edge of your area), which in this case is 3. The number at the top of your integral sign is your upper-bound (the larger x-value that defines the other vertical edge of your area), which in this case is 100. The equation that goes inside of your integral expression is the same equation that you were initially given, without the "y = ". Finally, you need to add "dx" after your equation in order to complete it.
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