To verify the identity we need the following identities:
i)
ii)
iii)
.
Also, we have know that
and
Thus,
By (ii) and (iii) we have:
by simplifying
and
Now,
is clearly -tanx.
Study? I’m not sure what this is asking
One A
y = e^x
dy/dx = e^x The f(x) = the differentiated function. Any value that e^x can have, the derivative has the same value. x is contained in all the reals.
One B
y = x*e^x
y' = e^x + xe^x Using the multiplication rule.
You want the slope and the value of the of y to be the same. The slope is y' of the tangent line
xe^x = e^x + xe^x
e^x = 0
This happens only when x is very "small" like x = - 4444444
y = e^x * ln(x) Using the multiplication rule again, we need the slope of the line with is y'
y1 = e^x
y1' = e^x
y2 = ln(x)
y2' = 1/x
y' = e^x*ln(x) + e^x/x So at x = 1 the slope of the line =
y' = e^1*ln(1) + e^1/1
y' = e*0+e = e
y = mx + b
y = ex + b
to find b we use y= e^x ln(x)
e^x ln(x) = e*x + b
e^1 ln(1) = e*1 + b
ln(1) = 0
0 = e + b
b = - e
line equation and answer.
y = e*x - e
Answer:
It there a picture
Step-by-step explanation:
Answer:
Step-by-step explanation:
Not exactly sure what your question is - I am assuming that it is something like:
Show/prove that for any integer x, x^2 - x is even.
Suppose that x is an even integer. The product of an even integer and any other integer is always even (x = 2n, so x * y = 2 n * y which is even. Therefore x^2 is even. An even minus an even is even. (The definition of an even number is that it is divisible by 2 or has a factor of 2. So the difference of even numbers could be written as 2*( the difference of the two numbers divided by 2); therefore the difference is even)
Suppose that x is an odd integer. The product of 2 odd numbers is odd - each odd number can be written as the sum of an even number and 1; multiplying the even parts with each other and 1 will produce even; multiplying the 1's will produce 1, so the product can be written as the sum of an even number and 1 - which is an odd number. The difference between two odd numbers is even - the difference between the even parts is even (argument above), the difference between 1 and 1 is zero, so the result of the difference is even.
x^2 is therefore even if x is even and odd if x is odd; The difference x^2 - x is even by the arguments above.
