Half Term 3 Flashcards
(53 cards)
What do you always need to add when integrating?
+c
What does dx mean?
With respect to x
What is the difference between a polynomial and an exponential?
In a polynomial x is the base, in an exponential it is the power
Where does an exponential always cross the y-axis (unless it is translated) and why?
It will always cross at 1 because anything to the power of 0 is 1
What does the graph look like when the base of an exponential is 1?
A flat line at y = 1
Why must the base of an exponential always be positive?
It cannot be negative because it is was it would jump between positive and negative values
Where is the asymptote for any exponential (unless translated)?
y = 0
What is special about Euler’s number?
The function of an exponential graph with the base of Euler’s number is equal to the gradient function of that graph
If y = e^kx then dy/dx = ?
5e^kx
What is the base of a log is it is not written?
10
loge() = ?
ln()
log a (y) + log a (x) = ?
log a (xy)
log a (y) - log a (x) = ?
log a (x/y)
log a (k^x) = ?
x log a (k)
log a (a) = ?
1
log a (1) = ?
0
lne^x = ?
x
e^lnx = ?
x
log (1/x) = ?
log (-x) = - log (x)
What does integrating the equation of a curve give you?
The area under a curve
Why do we use definite integrals?
We use definite integrals to get the area under a curve between two points
How do you change an exponential or polynomial graph to a linear graph?
By taking logs of both sides and using the data in log form
Why do we change exponential and polynomial graphs into linear graphs?
In order to make the data easier to manipulate and work with
y = b^x is a reflection of which other graph and along which line?
y = logb(x) along the line of y = x
