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Example Questions
Example Question #1 :How To Find The Meaning Of Functions
Take the limit
First, multiply the numerator and denominator byand it turns into
Factor the numerator and then cancel out the 'x+2'
After taking the limit, the answer is
Example Question #1 :Meaning Of Functions
If this limit is true, then what is the value of 'a'?
Factor the numerator
Cancel the, plug in the limit and then solve for 'a'
Example Question #3 :How To Find The Meaning Of Functions
We have a line described as。Find the minimum distance between the origin and a point on that line.
We have the originand a point疯狂的ated on the line. That point represents the minimum distance to the orgin. Apply the distance formula to these two points,
Plug in the line equation, take the derivative, set it equal to zero, and solve for x.
Use thisvalue to find
So we have the point, which is closest to the origin. We can now find its distance from that origin.
Example Question #1 :How To Find The Meaning Of Functions
We have the following,
What is c?
First, factor the numerator of the integrand.
Cancel out
Perform the integral and then solve for
Example Question #5 :How To Find The Meaning Of Functions
If, find
Taking the derivative of an integral yields the original function, but because we have a different variable in the integration limits, the variable switches
Example Question #2 :Meaning Of Functions
Evaluate
using integration identities:
Example Question #7 :How To Find The Meaning Of Functions
Evaluate
evaluate at
Example Question #1 :How To Find The Meaning Of Functions
Evaluate
Intergation by substitution
new endpoints:
New Equation:
at
Example Question #9 :How To Find The Meaning Of Functions
What is?
0
-1
1
undefined
0
The relationship betweenand x is an exponential relationship;is going toexponentially faster thanis going to。One way to prove this is to writeand use L'Hôpital's rule:
Example Question #10 :How To Find The Meaning Of Functions
Where isdiscontinuous? Are those discontinuities removable?
Removable discontinuity at, essential discontinuity at。
Removable discontinuities atand。
Removable discontinuity at, essential discontinuity at。
Essential discontinuities atand。
Removable discontinuities atand。
Removable discontinuity at, essential discontinuity at。
The rational functionhas a denominator with two roots,and。These are discontinuities.
Factoring both top and bottom and canceling a termtells us that this function is equal to
except at。这一点是removable discontinuity.is therefore an essential discontinuity where the ratio goes to。
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