Find the linearization L{x} of the function at a. x}=x3x2+5, a=2 Find the linearization L{x} of the function at a. x}: e4x, a: 9 Find the linear approximation L[x] of the function x] = y" 1 x at a = I]. Use L{x} to approximate the numbers 1.! 0.9 and 1.! 0.99. {Round your answers to four decimal places.) Use technology:r to graph fand the tangent line in the same viewing window. Find the differential of the function. y= ex dy = (a) Find the differential dy. y = ex/2 dy = (b) Evaluate dy for the given values of x and dx. x = 0, dx = 0.05 dy = (a) Find the differential dy. y = cos(nx) dy = (b) Evaluate dy for the given values of x and dx. (Round your answer to three decimal places.) X = - 1 dx = 0.01. dy =The radius of a circular disk is given as 27 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error (in cm*) in the calculated area of the disk. (Round your answer to two decimal places.) cm (b) What is the relative error? (Round your answer to four decimal places.) What is the percentage error? (Round your answer to two decimal places.) % When blood flows along a blood vessel, the flux F (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius R of the blood vessel. F = KR4 (This is known as Poiseuille's Law; we will show why it is true in a future chapter.) A partially clogged artery can be expanded by an operation called angioplasty, in which a balloon-tipped catheter is inflated inside the artery in order to widen it and restore the normal blood flow. Show that the relative change in F is about four times the relative change in R. dF F = KR4 = dR dF dR OF dR KR4 dR How will a 8% increase in the radius affect the flow of blood? A 8% increase in the radius corresponds to a(n) % increase in blood flow