SOLUTION: Which one of the following does not find the value of f ′(2) for f(x) = x2 + 3x + 1? f prime of 2 equals the limit as h approaches 0 of the quotient of the square of the

Algebra ->  Finance -> SOLUTION: Which one of the following does not find the value of f ′(2) for f(x) = x2 + 3x + 1? f prime of 2 equals the limit as h approaches 0 of the quotient of the square of the       Log On


   



Question 1001202: Which one of the following does not find the value of f ′(2) for f(x) = x2 + 3x + 1?
f prime of 2 equals the limit as h approaches 0 of the quotient of the square of the quantity 2 plus h plus 3 times the quantity 2 plus h plus 1 minus the quantity 2 squared plus 3 times 2 plus 1, and h
f prime of 2 equals the limit as h approaches 0 of the quotient of the square of the quantity 2 plus h plus 3 times the quantity 2 plus h plus 1 minus 2 squared plus 3 times 2 plus 1, and h
f prime of 2 equals the limit as x approaches 2 of the quotient of x squared plus 3 times x plus 1 minus 11, and the quantity x minus 2
All of these find the value for f ′(2).

Answer by KMST(5328) About Me  (Show Source):
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The square of the quantity 2 plus h plus 3 times the quantity 2 plus h plus 1
is %282%2Bh%29%5E2%2B3%2A%282%2Bh%29%2B1=f%282%2Bh%29 .
The quantity 2 squared plus 3 times 2 plus 1
is 2%5E2%2B3%2A2%2B1=f%282%29=11 .


CHOICE # 1:
The limit as h approaches 0 of
the quotient of
the square of the quantity 2 plus h plus 3 times the quantity 2 plus h plus 1
minus
the quantity 2 squared plus 3 times 2 plus 1,
and h
is .
That is by definition %22f%27%282%29%22 .

CHOICE # 2 does not find the value of %22f%27%282%29%22 :
The limit as h approaches 0 of
the quotient of
the square of the quantity 2 plus h plus 3 times the quantity 2 plus h plus 1
minus 2 squared
plus 3 times 2
plus 1,
and h
is .
That is not %22f%27%282%29%22=lim%28h-%3E0%2C%28f%282%2Bh%29-11%29%2Fh%29 .

CHOICE # 3:
The limit as x approaches 2 of
the quotient of
x squared plus 3 times x plus 1
minus 11,
and
the quantity x minus 2
is lim%28x-%3E2%2C%28%28x%5E2%2B3x%2B1%29-11%29%2F%28x-2%29%29=lim%28x-%3E2%2C%28f%28x%29-11%29%2F%28x-2%29%29=lim%28x-%3E2%2C%28f%28x%29-f%282%29%29%2F%28x-2%29%29 .
That is by definition %22f%27%282%29%22 .