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Analysis
Analysis
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1
What are you going to do?
Ace the exam
Write down some brilliant answers
Destroy the exam
2
Determine the interval of convergence of \sum _{n=1}^∞\frac{\left(5x-4\right)^n}{n^3}
I=\left(\frac{3}{5,}1\right)
I=\left[\frac{3}{5,}1\right)
I=\left[\frac{3}{5},1\right]
I=\left(\frac{3}{5,}1\right]
3
My favorite theorem is...
Fubini's Theorem
Mean Value Theorem
The inverse is unique
Fundamental Theorem of the Calculus
4
Which of the following do u use to calculate the inverse function?
\left(f\circ f^{-1}\right)\left(x\right)=x
\left(f^{-1}\circ f^{ }\right)\left(x\right)=x
5
What is very important for the exam?
Precise notation
Being able to reproduce the proofs from the list
Sound motivation of steps
Chill the day itself. try to go to bed early
6
Is the following function differentiable everywhere?
Yes
No
7
Identify the discontinuities, if any.
Discontinuity at x = 1
No discontinuities
Discontinuity at x = 0
Discontinuity at x = 0 and x = 1
8
Is this a region of type I, type II or neither?
Type II
Both
Type I
Neither
9
MEMORY CHECK: determine the radius of convergence of \sum_{n=1}^∞\frac{\left(5x-4\right)^n}{n^3}
I=\frac{1}{5}
I=\left[\frac{3}{5,}1\right)
R=\frac{1}{5}
R=\left(\frac{3}{5,}1\right)
10
Why can we not use Fubini here?\int_0^1\int_{\frac{x}{2}}^4x^2dydx
Some other condition is not satisfied
We can use Fubini
Because our function is not continuous everywhere.
Because \frac{x}{2} in the integration limit is not a constant.
11
Determine if the following series is divergent or convergent \sum_{n=0}^∞\frac{\ln\left(n\right)\cdot n}{\sqrt{n}}
Convergent
Divergent
Absolutely no clue
12
Give a description of the concept continuity
Looking for kinks in the graph
Continuity implies differentiability
Calculating derivatives
Comparing limits and function values
13
What is the first thing you do when you see an improper integral?
Find the antiderivative
Start solving it
Add +C
Take the limit
14
Is this a region of type I, type II or neither of the two?
Both
Type II
Type I
Neither
15
Where is the following function undifferentiable?
At x = 1
At x = 1 and x = 0
At x = 0
