All Calculus 2 Resources
Example Questions
Example Question #103 : Vector Calculations
Calculate
Calculate the dot product of the 2 vectors.
In general,
Solution:
Example Question #104 : Vector Calculations
Calculate
Calculate the sum of vectors.
In general,
Solution:
Example Question #105 : Vector Calculations
Calculate
Calculate the dot product of the 2 vectors.
In general,
Solution:
Example Question #265 : Vector
Calculate
Calculate the dot product of the 2 vectors.
In general,
Solution:
Example Question #611 : Parametric, Polar, And Vector
Find the sum of the vectors
and if
.
For the two vectors
and
The sum of the two vectors a+b is
For the vectors u and v in this problem the sum u+v is
Example Question #1 : Derivative Review
Evaluate the limit using one of the definitions of a derivative.
Does not exist
Evaluating the limit directly will produce an indeterminant solution of
.The limit definition of a derivative is
. However, the alternative form, , better suits the given limit.Let
and notice . It follows that .Thus, the limit is
Example Question #2 : Derivative Review
Evaluate the limit using one of the definitions of a derivative.
Does not exist
Evaluating the derivative directly will produce an indeterminant solution of
.The limit definition of a derivative is
. However, the alternative form, , better suits the given limit.Let
and notice . It follows that . Thus, the limit is .
Example Question #1 : Derivatives
Suppose
and are differentiable functions, and . Calculate the derivative of , atNone of the other answers
None of the other answers
The correct answer is 11.
Taking the derivative of
involves the product rule, and the chain rule.
Substituting
into both sides of the derivative we get.
Example Question #4 : Definition Of Derivative
Evaluate the limit
without using L'Hopital's rule.
If we recall the definition of a derivative of a function
at a point , one of the definitions is.
If we compare this definition to the limit
we see that that this is the limit definition of a derivative, so we need to find the function
and the point at which we are evaluating the derivative at. It is easy to see that the function is and the point is . So finding the limit above is equivalent to finding .We know that the derivative is
, so we have.
Example Question #1 : Derivatives
Approximate the derivative if
where .
Write the definition of the limit.
Substitute
.
Since
is approaching to zero, it would be best to evaluate when we assume that is progressively decreasing. Let's assume and check the pattern.
The best answer is:
Certified Tutor
Certified Tutor
All Calculus 2 Resources
