All Calculus 1 Resources
Example Questions
Example Question #31 : How To Find Differential Functions
Solve for when
using the chain rule:
multiply the constant 9 into the second function to simplify answer
Example Question #32 : How To Find Differential Functions
Solve for when
using the logarithm identities change the equation to base 10:
using lograthim identities simplify the numerator:
differentiate
Simplify
Example Question #215 : Functions
Solve for when
Using the product rule:
FOIL
Combine like-terms
Example Question #33 : How To Find Differential Functions
Solve for using implicit differentiation if
Differentiate the equation
Simplify
place all terms with on one side and the other terms on the other side
Simplify
Divide and solve for
Example Question #34 : How To Find Differential Functions
Solve for using the Mean Value Theorem, rounded to the nearest hundredth place when
on the interval
Mean Value Theorem (MVT) = on
Example Question #32 : How To Find Differential Functions
Evaluate the limit:
Attempting to evaluate directly (plug in -1 for ) results in the indeterminate form:
Further analysis is required:
This final form can be evaluated directly:
Example Question #33 : How To Find Differential Functions
Evaluate the limit:
Attempting to evaluate directly (plug in 2 for ) results in the indeterminate form:
Further analysis is required:
This final form can be evaluated directly:
Example Question #37 : How To Find Differential Functions
Evaluate the limit:
We evaluate the limit directly (plug in 3 for ) and obtain:
from which we determine that the the function has a vertical asymptote at this point (it goes off to positive or negative infinity). The limit Does Not Exist.
Example Question #38 : How To Find Differential Functions
Given:
Evaluate the limit:
This limit can be evaluated directly.
Recall that
So:
Example Question #39 : How To Find Differential Functions
Given:
Evaluate the limit:
First observe that
Multiplying by we obtain:
Limit of product is the product of limits:
From the Pre-Question Text:
So:
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