A1 represents the first term
d represents the common difference.....and since the common difference is 3, u have to add 3 to each term to find the next term....because with an arithmetic sequence u add to find the next term, whereas, in a geometric sequence u multiply to find the next term
5...first term
5 + 3 = 8...2nd term
8 + 3 = 11...3rd term
11 + 3 = 14...4th term
ur answer is B
The point-slope form:
The formula of a slope:
We have the points (-4, -1) and (5, 7). Substitute:
If tangent to the curve y = √x is parallel to the line y = 8x, then this implies that the tangent to y = <span>√x has the same slope as the line y = 8x. In other words, the derivative (slope) function of y = √x is equal to the slope of the line y = 8x, which is m = 8. Hence y' = 8 once we find y'
y = </span><span>√x = x^(1/2)
Applying the power rule and simplifying, we find that the derivative is
y' = 1/(2</span>√x)
Now remember that y' must equal 8
1/(2<span>√x) = 8
Multiplying both sides by 2</span><span>√x, we obtain
1 = 16</span><span>√x
Dividing both sides by 16, yields
</span><span>√x = 1/16
But wait a minute, √x = y. Thus 1/16 must be the y-coordinate of the point at which the tangent to y = √x is drawn.
Squaring both sides, yields
x = 1/256
This is the x-coordinate of the point on the curve where the tangent is drawn.
</span><span>∴ the required point must be (1/256, 1/16)
GOOD LUCK!!!</span>