A and B are the points on the curve y=2^x with the coordinates 3 and 3.1 respectively. Find the gradient/slope of the chord AB and stating the points you use, find the gradient of another chord which will give a closer approx. to the gradient/slope of the tangent to y=2^x at A. thanks

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A and B are the points on the curve y=2^x with the coordinates 3 and 3.1 respectively. Find the gradient/slope of the chord AB and stating the points you use, find the gradient of another chord which will give a closer approx. to the gradient/slope of the tangent to y=2^x at A. thanks

Mathematics
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A = (3, 2^3) = (3,8) B = (3.1,2^(3.1)) = (3.1, 8.57) slope = .57/.1 = 5.7
since a is at 3; use a closer value of x that is between 3 and 3.1; such as 3.01
as you get closer and closer to A, which is (3,8); you will approach the limit that is equal to the slope at 'A'; also known as the derivative of y = 2^x at x=3

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does that help?
wait let me read it through a few times :S
how did you get the slope? where did you get the numbers from 0.57/0.1=5.7???
you are given a function for y: 2^x correct? At point A it says that x=3 and at point B, x=3.1 right?
yes
point A = (3,2^3) point B = (3.1, 2^(3.1))
B-A gives you the slope: x , y -------------- 3.1 , 2^(3.1) -3 , - 2^3 --------------- ( .1 , .57418...) slope = y/x = .57/.1 = 5.7/1 = 5.7
thanks
youre welcome :)

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