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The point P(6, -4) lies on the curve y = 5 - x (a) If Q is the point x, find the slope of the secant line PQ (correct to six decimal places) for the following values of x. 5 - x (i) 5.9 mPQ = (ii) 5.99 mPQ = (iii) 5.999 "PQ = (iv) 5.9999 mPQ = (v) 6.1 MPQ = (vi) 6.01 MPQ = (vil) 6.001 mPo = (viil) 6.0001 mPQ (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(6, -4). (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(6, -4).

The point P(6, -4) lies on the curve y = 5 - x (a) If Q is the point x, find the slope of the secant line PQ (correct to six decimal places) for the following values of x. 5 - x (i) 5.9 mPQ = (ii) 5.99 mPQ = (iii) 5.999 "PQ = (iv) 5.9999 mPQ = (v) 6.1 MPQ = (vi) 6.01 MPQ = (vil) 6.001 mPo = (viil) 6.0001 mPQ (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(6, -4). (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(6, -4).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The point P(6, -4) lies on the curve y = 5- x 4 (a) If Q is the point (x, find the slope of the secant line PQ (correct to six decimal places) for the following values of x. 5 - x (1) 5.9 mPQ !3! (ii) 5.99 mpQ = (ii) 5.999 mpQ %3D (iv) 5.9999 mPo = (v) 6.1 mpQ = (vi) 6.01 mpo = (vii) 6.001 mpQ %3D (viil) 6.0001 mpQ %3D (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(6, -4). m 3D (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(6, -4).
Transcribed Image Text:The point P(6, -4) lies on the curve y = 5- x 4 (a) If Q is the point (x, find the slope of the secant line PQ (correct to six decimal places) for the following values of x. 5 - x (1) 5.9 mPQ !3! (ii) 5.99 mpQ = (ii) 5.999 mpQ %3D (iv) 5.9999 mPo = (v) 6.1 mpQ = (vi) 6.01 mpo = (vii) 6.001 mpQ %3D (viil) 6.0001 mpQ %3D (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(6, -4). m 3D (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(6, -4).
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