help with 2 math probs?

Question

lolokrat · Answer

#1

lolokrat · Answer

i know a,c,d but having trouble w/ b & e

SmokeyBrown · Answer

Let's check (a) since I'm not so sure about that one
f(9+1) would be f(10) which is
2 + 10 + 10^2 = 112
And then f(9) + f(1) would be
2 + 9 + 9^2 = 92
+
2 + 1 + 1^2 = 4
=96
112 =/= 96, so the answer for (a) would be no, the two are not equal.

Moving along, you said you were having trouble with (b) and (e)...
Part (b) asks us to evaluate f(x+h), which we can find by replacing the "x"s in the equation with (x+h) to get:
2 + (x+h) + (x+h)^2 =
2 + (x+h) + (x^2 + 2xh + h^2)

For part (e), we can take the answer to part (b), subtract the original function f(x) and divide the result by h:
[2 + (x+h) + (x^2 + 2xh + h^2) - (2 + x + x^2)]/h =
[(2-2) + (x - x) + h + (x^2 -x^2) + 2xh + h^2]/h =
(h + 2xh + h^2)/h = 
1 + 2x + h
If I am not mistaken, that should be the simplification of that expression

lolokrat · Answer

ah, i screenshotted the problem before i plugged in my answer choice to a, but thank you for the explanation!

you are absolutely correct but could you please explain how in part b's solution you got 2xh?

SmokeyBrown · Answer

@lolokrat wrote:

ah, i screenshotted the problem before i plugged in my answer choice to a, but thank you for the explanation! you are absolutely correct but could you please explain how in part b's solution you got 2xh?

Apologies for the late response. For that portion of the expression, we have (x + h)^2 or (x + h) * (x + h) If we multiply out all of the terms, we get: x*x + x*h + x*h + h*h Which simplifies to: x^2 + xh + xh + h^2 == x^2 + 2xh + h^2

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