Topic 2 - Term Test 1 Flashcards
(9 cards)
2.4
How to determine continuity?
- Plug in point into equation
- Find right and left hand limits
- If they are equal, function is continous
2.4
How to solve IVT questions that ask to show that the function has at least one root? What would the conclusion be?
0, State that root is c so that f(c) = 0
1. Pick easy values (like 0, -1, and 1) and ensure function is continous between the two values that you pick
2. Sub in values and ensure one is above 0 and one is below
Then there is a c that is an element fo [0, 1] satisfying f(c) = 0
2.4
How to determine if function is positive or negative infinity?
lim as x approches 4+ of 2x/x-4
sub in number slightly above 4 and denominator will be negative so answer is negative infinity
2.4
Determine what kind of discontinuity of
tan(3x-2pi/4)
Take the right hand and left hand limits. Do sign analysis to determine what the infinity will be
2.4
What should you ask yourself before using IVT
Is my function continous within this domain?
2.3
When using squeeze theorem, can restrictions be thought of as domain or range?
Range
2.4
Question asks find the value of variable that makes the function continuous everywhere at x =3, how should you solve
Compute f(3) and the limits as x approches 3 from both teh left and the right
Then set one of these limits that should have no variable to the one that is the variable and this should all be equal
2.2
Limit as x approches 0 of x/x
Evaluate x/x as 1 and using the limit laws the answer is 1
2.3
Solving squeeze theorem questions, what should you remember about establishing the range
Remember that if you are multiplying by another function you need to consider the range of that function. for example multipling by sin^2, the function cannot have the range -1 to 1 becuase suaring a value only has positive values, so it has to be 0 to 1 now
