9514 1404 393
Answer:
4) 6x
5) 2x +3
Step-by-step explanation:
We can work both these problems at once by finding an applicable rule.
where O(h²) is the series of terms involving h² and higher powers. When divided by h, each term has h as a multiplier, so the series sums to zero when h approaches zero. Of course, if n < 2, there are no O(h²) terms in the expansion, so that can be ignored.
This can be referred to as the <em>power rule</em>.
Note that for the quadratic f(x) = ax^2 +bx +c, the limit of the sum is the sum of the limits, so this applies to the terms individually:
lim[h→0](f(x+h)-f(x))/h = 2ax +b
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4. The gradient of 3x^2 is 3(2)x^(2-1) = 6x.
5. The gradient of x^2 +3x +1 is 2x +3.
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If you need to "show work" for these problems individually, use the appropriate values for 'a' and 'n' in the above derivation of the power rule.
Answer:
y=3/5x+3
Step-by-step explanation:
Answer:
y = (1/2)x - 3 Answer A is closest.
Step-by-step explanation:
Two points on the line are (0, -3) and (4, -1). Notice that I've intentionally chosen "nice" points whose coordinates are integers; this makes the math easier. The point (1, -5/2) is also on the line if you want to use it, but the math's a bit more complicated.
Going from (0, -3) to (4, -1), x increases by 4 and y increases by 2. Hence, the slope of this line is m = rise / run = 2/4, or m = 1/2.
The slope-intercept formula for the equation of a straight line is the most convenient to use here, since we can tell immediately from the graph that the y-intercept is (0, -3):
y = (1/2)x - 3
Answer A should be y = (1/2)x - 3 for improved legibility. 1 2 x is not correct as a way to express (1/2)x.
200=x-4 original equation
204=x addition property of equality (add 4 on both sides)
x=204 symmetric property