Pls help ASAP. Pls show work. Find an equation of the tangent line to the function y = 4x at the point P(1, 4).SolutionWe will be able to find an equation of the tangent line { as soon as we know its slope m. The difficulty is that we know only one point, P, on , whereas we need two points to compute the slope. But observe that we can compute an approximation to m by choosing a nearby point Q Ax) on the parabola (as in the figure below) and computing the slope m of thesecant line PQ. [A secant line, from the Latin word secans, meaning cutting, is a line that cuts (intersects) a curve more than once.]We choose x÷1 so that Q P. Then,4x - 4Po =X-1For instance, for the point Q(1.5, 20.25) we have the following.%3DmPQinThis suggests that the slope of the tangent line e should be m =The tables below show the values of me for several values of x dose to 1. The closer Q is to P, the cdoser x is to 1 and, it appears from the tables, the closer men is tompQ2.601.532.57.51.118.56413.75610116.2429915,7621.00116.02499915.976We say that the slope of the tangent line is the limit of the slopes of the secant lines, and we express this symbolically by writing the following.lim (m) = mandlimAssuming that this is indeed the slope of the tangent line, we use the point-slope form of the equation of a line (see Appendix B) to write the equation of the tangent line through (1, 4) as the following.-1)ory-627 AM2/15/2022in

We will use point - slope form to find equation of tangent line to curve through given point

Find an equation of the tangent ine to the function y 4at the point P1, 4) Solution We will be able to find an equation of the tangent ine t as soon as we know its slope m. The difficoulty is that we know only one point, P, on , whereas we need twe points to compute the slope. But observe that we can cempute an approimation to m by choosing a neart secant ine PQ. (A secant line, from the Latin word secans, meaning cutting, is a line that cuts (intersects) a curve more than once) f computing the the We chooserlso that Q P. Then For instance, for the point O1.5, 20.25) we have the followinng This suggests that the slope of the tangent ne shoull bem The tables below show the values of m for several values of x dlose to L. The doser Qis to P the dloser is to 1 and, it appears from the tables the closer mis to 60 32.5 7.5 18.564 13.756 16.242 99 15.762 999 1.001 16.024 15.976 secant ines, and we express this symbolically by writing the following We say that the slope of the tangent ine is the limt of the slopes of the and Assuming that this is indeed the slope of the tangnt ne, we use the point lope form of the equation of a ne (seeAppendi 8) o wite the eguation of the tangent e through (, 4)as the foowing O-(O)

Find an equation of the tangent ine to the function y 4at the point P1, 4) Solution We will be able to find an equation of the tangent ine t as soon as we know its slope m. The difficoulty is that we know only one point, P, on , whereas we need twe points to compute the slope. But observe that we can cempute an approimation to m by choosing a neart secant ine PQ. (A secant line, from the Latin word secans, meaning cutting, is a line that cuts (intersects) a curve more than once) f computing the the We chooserlso that Q P. Then For instance, for the point O1.5, 20.25) we have the followinng This suggests that the slope of the tangent ne shoull bem The tables below show the values of m for several values of x dlose to L. The doser Qis to P the dloser is to 1 and, it appears from the tables the closer mis to 60 32.5 7.5 18.564 13.756 16.242 99 15.762 999 1.001 16.024 15.976 secant ines, and we express this symbolically by writing the following We say that the slope of the tangent ine is the limt of the slopes of the and Assuming that this is indeed the slope of the tangnt ne, we use the point lope form of the equation of a ne (seeAppendi 8) o wite the eguation of the tangent e through (, 4)as the foowing O-(O)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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