3. For f(x)=x²-2x+3, find the slope of the tangent line at the point P for which x=1 using the limit of the mpg. X у MpQ .9 .99 .999 1.001 1.01 1.1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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3. For f(x)=x² −2x+3, find the slope of the tangent line at the point P for which x=1 using
the limit of the mpo ·
X
у
MpQ
.9
.99
.999
1.001
1.01
1.1
Transcribed Image Text:3. For f(x)=x² −2x+3, find the slope of the tangent line at the point P for which x=1 using the limit of the mpo · X у MpQ .9 .99 .999 1.001 1.01 1.1
Expert Solution
Step 1: Definitions

Here, y = f(x) 

             = x- 2x + 3

Now, the slope of the tangent at P (for which x = 1) is given by

          mPQ = limx→1 fraction numerator y minus y open parentheses 1 close parentheses over denominator x minus 1 end fraction 

                   = limx→1 fraction numerator y minus 2 over denominator x minus 1 end fraction    [ y(1) = 2 ]

  So, for the given values of x in the table, we calculate the y-values and the corresponding ratios. 

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